At first glance it really does seem that these are two different things. Presumed possession is learned from the reasoning that “the one who feels the pain goes to the physician,” as explained in Bava Kamma 46, whereas an original presumption is learned from the laws of house-plagues. The problem is that there are many formulations among the medieval authorities that treat presumed possession too as a certain kind of presumption — “the presumption of financial possession” — and even more so because we find that laws of original presumption were applied to the rule of presumed possession, as explained:
A. In Tosafot Rid on Kiddushin 79, presumed possession combines to create a double disadvantage, and that applies only to presumptions (see also Ketzot HaChoshen 34:5 and Netivot there, subsection 15, on this).
B. Tosafot at the beginning of “HaMani’ach” 27 wrote, explaining why in monetary law we do not follow the majority, “because there is a minority and a presumption…” — aside from the fact that they plainly call presumed possession a presumption, their meaning is apparently that it has the law of a presumption, and that applies only to a presumption (and Rabbi Akiva Eiger, second edition, sec. 103, says this explicitly).
C. The conclusion of the sugya of “if a priest seized it” is that we take it away from him (according to most medieval authorities), and this makes sense only if we say that there is some sort of legal determination in favor of the first possessor; because if it is just “the burden of proof is on the claimant,” why shouldn’t the considerations flip in favor of the second possessor who is now holding it? So clearly there is some kind of legal determination here.
And there are more proofs of this kind, and Maharik 72 explicitly writes that this is an original presumption, see there.
But all this is very difficult conceptually, because there is no biblical decree at all teaching that presumed possession contains any sort of legal determination, certainly not a “presumption,” and in Bava Kamma all that is explained is mere reasoning. Even aside from that, it is hard to understand calling it a presumption, because a presumption makes sense, for example, with a presumption of prohibition — if it was prohibited yesterday, it will be prohibited today — or that yesterday’s owner is today’s owner. But with presumed possession, today he is merely physically holding it, and there is no logic in saying that because he held it yesterday, today he should be considered the owner??
Thank you in advance..

As I said, beyond the formulations of the medieval authorities that you cited, which also need analysis, the accepted view is different (as in Kuntres HaSfeikot). But you are raising a discussion within the approach that says it is the same thing, so let’s go with you.
One could say that according to this approach, the statement “the one who feels the pain…” is reasoning that explains why financial possession is in fact an original presumption. I am in possession of the money, and that reasoning says that if you want to change the situation, bring proof. In other words, unless you bring proof that changes the situation, we leave it as it is. There you have it: we have arrived at an original presumption.
As for your question what is the reasoning for turning possession into ownership — here you are bringing in the inquiry of the later authorities whether a ruling of “the burden of proof is on the claimant,” based on possession, really turns the winner into the owner (a practical difference for an etrog on the first day). Even if you are right, there is still room to say that the original presumption extends the possession and the state of being the holder, but not the ownership. Meaning: I am allowed to continue holding the item, while ownership itself is indeed open to discussion. That is the approach that “the burden of proof is on the claimant” does not create ownership. But one can also say that once we reach the conclusion that I am allowed to keep the money, it is now also considered mine, and we arrive at ownership. Somewhat like Rabbi Shimon Shkop’s reasoning that in monetary law what determines matters is the legal ruling, not the factual truth.

In my opinion the matter is still quite different. With an original presumption I say that yesterday there was a certain definite and absolute status (for example, prohibition), and today I am in doubt, so the presumption tells me not to change it. But with presumed possession there was never any definite status at all, and now I am holding it and want to become the owner based on the present moment. There is no prior status here to extend. And I also don’t think the reasoning of “not changing” applies. The Rabbi wrote that we extend the possession itself, or the ownership that follows from it — but the question is how that itself happens. How does the fact that I am holding an object give me ownership or permission to keep it? On that you cannot say “presumption,” because up to this point there was nothing here. And the reasoning of “do not change” also does not apply, because “do not change” is said only after some sort of prior determination.

That is not correct. The presumption of life, or even the presumption regarding a plague-mark from which the whole idea is learned (in the first chapter of Chullin), are not presumptions about legal status but about facts.

That wasn’t my claim. Obviously a presumption can also be stated about facts. I was only pointing out that in presumed possession it is different: there is no definite state that existed yesterday, like a plague-mark, that we are extending into today. I am holding it now, at this very second, and I want to say there is a presumption about that. Even in factual terms: I seized it just now, and the doubt concerns the present — whether this current holding is permitted / creates ownership. About that it does not make sense to speak of a presumption.

I don’t understand what the discussion is about. I was in possession, and the original presumption says that I may continue to be in possession. Is that enough to create certainty, or not? I already noted that there is disagreement about this.
Let the chooser choose.

After going over this again, it is still not clear whether the mere fact that someone is “in possession” is in itself a sufficient reason for the money to be his. Why do we need to invoke presumption at all? After all, there is permission to use it simply because he is holding it. And one cannot say that the presumption comes to give him definite status, because if possession only gave him a doubt-based claim, then a presumption whose whole purpose is not to change the existing state would at most say: continue not taking it away from him despite the doubt. But there would never be a leap to definite status. And if we say that being in possession is indeed not a real reason to leave the money with him, but only because of the presumption, and we explain the Talmud in Bava Kamma as the Rabbi wrote — that “the one who feels the pain” means not changing the current state, that is, presumption — then I return to my original question: if the only reason is presumption, how does the physical fact that a person is holding something (which, as I argued, creates no legal status in itself) become a presumption that grants him permission to use it or alternatively creates ownership? Surely it has to begin from something..?

I don’t understand the question. Reuven was holding the money, and now Shimon is claiming it from him. Before the claim, it is obvious that Reuven has the right to use it (after all, he claims it is his; there is no presumption without a claim). So as long as Shimon has not challenged him, who would stop him from using it? This is not a doubt but a certainty. Now a claim arises that creates doubt. The presumption comes and says that he may continue using it as before. That is indeed only an extension of the possession and no more. But from the moment a claim arises that creates doubt — which did not exist beforehand — you can continue the permission of use based on possession only if you activate the mechanism of original presumption, which extends the prior state.
I don’t understand what the problem is here.

You are speaking about a particular case where I was the owner and only now a doubt arose. In that case it is obvious that there is a “presumption,” either because of the presumption that what is under a person’s control is his, or because of prior ownership. But that is not what I was talking about. In such a case there is no need to invoke presumed possession at all (and by the way, here according to everyone the money is certainly his)… I am talking about bare presumed possession, such as in “if a priest seized it”: there is doubt about a firstborn animal, no one has prior ownership, and the rule is that we go after the current possessor, and it is explained that this is like a presumption. That is what is puzzling, because it has no connection at all to presumption.
Likewise in “two are holding” and in the case of “an ox that gored a cow,” where the doubt is whether an obligation ever came into being at all — there is no connection to prior ownership, only to simple possession.

But possession before the doubt arose — Tosafot at the beginning of Bava Batra writes that only such possession is effective — gives definite permission of use, not doubtful permission. Even if I was not the owner, I am allowed to use what I am holding, especially if I have a claim along with the possession (possession with a claim). And even if there is no presumption that what is under a person’s hand is his, that makes no difference at all. That presumption is relevant only after a doubt has arisen. Before that, possession alone is enough to grant permission of use…

Okay, and what do we say about possession after the doubt has arisen??

After the doubt has arisen, possession has no force. Certainly not enough to give it definite legal status.

In “if a priest seized it,” “two are holding,” and the like, it is possession after the doubt arose, and it still works. What would you answer there..?

At the moment I am not fluent in this sugya. But why are you assuming that this approach must fit with the approach that sees presumed possession as an original presumption? You yourself said there are views like that and others who disagree. Those views would not hold that possession after the doubt arose is effective.

Because it is contradicted by the Talmud… It is not clear how that opinion would explain the law of presumed possession after the doubt.

I didn’t understand. According to Tosafot on Bava Batra, there is no effective seizure after the doubt arose. So how would they explain the Talmudic passages? Clearly, you are forced to say that at least in their view those cases are not seizure after the doubt arose (except in a situation where a person takes the law into his own hands, but that is not our discussion).
As for “two are holding,” I do not see why that must necessarily be possession after the doubt arose. And in any case, in “if a priest seized it,” as is well known, there is a dispute whether seizure is actually effective.

For your information, there is the Chazon Ish who explains that presumed possession is the simple default state of the matter, and Rav and Shmuel disagree whether it is a definition within the doubt or a legal determination: according to Shmuel it is a rule within the doubt, and therefore we follow the majority first, and only afterward it is not relevant to speak of presumption; whereas according to Rav we begin with the current possessor, since that too is a definition within the doubt, and only afterward majority no longer applies.
But regarding the distinction between presumption and presumed possession, in Shema’ata he wrote that presumption relates to the past, while presumed possession relates to the present; and if you want, he elaborated further there in explaining presumption.

And by the way, I really enjoyed your back-and-forth on the topic.