There is a practical difference regarding the laws of overriding, for example in Maimonides, Laws of Forbidden Mixtures, chapter 10, halakha 29:
One who sees a Torah-level forbidden mixture on his fellow—even if he is walking in the marketplace—jumps on him and tears it off him immediately. Even if he was his teacher who taught him wisdom—for human dignity does not override an explicit prohibition stated in the Torah.

That implies that if it were a prohibition not explicitly stated in the Torah, human dignity would override it.

Another practical difference I just remembered is whether subduing one’s inclination overrides the commandment or not. For example, Babylonian Talmud, Bava Metzia 32b:
If one person is beloved and needs unloading, and another is disliked and needs loading, the commandment concerning the one you dislike takes precedence, in order to subdue one’s inclination. And if you would think that preventing animal suffering is Torah-level—surely that would be preferable? Even so, subduing one’s inclination is preferable.

If it were an explicit commandment, I don’t think subduing one’s inclination would override it.

I’m not sure that’s what he means. There are other sources for the idea that an explicit prohibition is more severe (like Ran on Nedarim 8a, who writes that an oath takes effect on a prohibition that is not explicit and is derived by exposition). Maimonides too may perhaps mean a prohibition derived by exposition, which in his view is rabbinic. Otherwise it’s hard for me to understand the source for his distinction. The Talmud distinguishes between passive omission and positive action, but not between explicit and non-explicit. We’d need to check the commentators there.

As for subduing the inclination, I also don’t see the source for a difference between explicit and non-explicit. There the distinction is between Torah-level and rabbinic, and in the conclusion in both cases subduing the inclination is preferable.

I found another distinction by Maimonides between an explicit prohibition and one that is not explicit:
Maimonides, Laws of Oaths, chapter 5:
And why is he not lashed for a vain oath? Because it is possible for those others who hear from him that his oath will be fulfilled, and it turns out that when he is warned at the time he swears, it is an uncertain warning, for one is not lashed for an uncertain warning unless the prohibition involved is stated explicitly in the Torah, as will be explained in the Laws of Sanhedrin.

According to Maimonides, one is not lashed for an uncertain warning, unless it is a warning for a prohibition explicitly stated in the Torah.

Maimonides’ words here are very unclear. What difference is there between an uncertain warning for an explicit prohibition and for one that is not explicit? Therefore I am inclined to think like the Lechem Mishneh there, who explained that according to Maimonides there is doubt whether he violated the prohibition of a vain oath or a false oath, and therefore it is an unclear prohibition, which counts as an uncertain warning, and he is not lashed. But an explicit prohibition—that is, one about which there is no doubt—there the warning is not an uncertain warning and therefore he is lashed. But there is no general rule that if it is an explicit prohibition and there is an uncertain warning, he is lashed for it, as the simple meaning of his wording suggests. According to this, there is no distinction here at all between an explicit prohibition and a non-explicit one, but rather between a clear prohibition and a doubtful prohibition.

I found another Maimonides along the same lines in his Commentary on the Mishnah:
Mishnah, tractate Sanhedrin, chapter 7, mishnah 6:
One who worships idolatry—whether by serving, slaughtering, burning incense, pouring a libation, bowing, accepting it upon himself as a god, or saying to it, “You are my god”—but one who embraces it, kisses it, honors it, sprinkles before it, washes it, anoints it, dresses it, or shoes it transgresses a prohibition. One who vows by its name or upholds something by its name transgresses a prohibition. One who exposes himself to Baal Peor—that is its worship; one who throws a stone to Mercury—that is its worship.
Commentary on the Mishnah by Maimonides, tractate Sanhedrin, chapter 7:
“And one who embraces it” means one who hugs that image; the Aramaic translation of “and he embraced him” is “and he hugged him.” And these things of which he said that one transgresses a prohibition—this is correct, and they are included in the general statement, “You shall not worship them,” but one does not receive lashes for them, because their prohibition is not explicit. But one is liable to lashes for one who vows by its name or fulfills by its name, for Scripture says, “And the name of other gods you shall not mention,” etc. And even if one intended, when exposing himself to Peor or throwing a stone to Mercury, to degrade that which is worshipped and treat it with contempt, he is still liable to bring a sin-offering. And there is no difference between throwing a stone to it or removing a stone from before it, because in both ways it is worshipped.

And another one:
Maimonides, Laws of Slaughtering, chapter 5:
[1] We have already explained in the Laws of Forbidden Foods that the terefah stated in the Torah is an animal inclined to die, and it is only called terefah because Scripture spoke of the usual case, such as where a lion tore it and the like, and broke it, yet it has not died.
[2] There are other illnesses there too, and if they occur it is considered terefah, and they are a law given to Moses at Sinai. Eight kinds of terefot were said to Moses at Sinai, and these are they: attacked by a predator, perforated, lacking, removed, severed, torn, fallen, and broken.
[3] Even though all of them are a law given to Moses at Sinai, since the only one explicit in the Torah is attacked by a predator, they were stricter about it, and any doubt that arises regarding attacked by a predator is forbidden, whereas with the other seven kinds of terefot there are doubts that are permitted, as will be explained.

And I also found in Maimonides’ Commentary on the Mishnah, tractate Makkot, chapter 3:
The fifth category is a prohibition inferred from a positive commandment, such as with the High Priest, where it says, “And he shall take a wife in her virginity,” implying that he is forbidden to marry a non-virgin. But since we were not told explicitly, “He shall not take a non-virgin,” if he transgressed and married a non-virgin, he is not liable to lashes as is one who married a widow, divorcée, zonah, or halaláh. Similarly, with an Egyptian and an Edomite, where it says, “Children born to them, the third generation…” we know that the first and second generations may not enter the congregation. But if one transgressed, he is not liable to lashes, because the prohibition was not stated explicitly, as it was with “A mamzer shall not enter,” “An Ammonite or Moabite shall not enter.”

The sixth category is a general prohibition, for which one is not lashed. This is a prohibition not stated explicitly but learned from other statements, as they say in many places: “It was not stated as an explicit prohibition, but was inferred.” For example, it says: “Bread, parched grain, and fresh grain you shall not eat.” What follows from this is that you shall not eat the new crop of grain. But if one ate only parched grain, we do not give him two sets of lashes, one for “you shall not eat parched grain” and another for “you shall not eat the new crop”; rather, one set of lashes for parched grain. And similarly, if he ate fresh grain, for fresh grain. Likewise, if a nazirite ate grape pits or grape skins, he is not liable to two sets of lashes, one because grape pits are explicit, and the second because of “anything produced by the grapevine,” because that is a general prohibition. If it had said explicitly, “From anything produced by the grapevine he shall not eat, from grape pits to skins he shall not eat,” then he would have been liable for eating grape pits twice, and likewise for skins, and likewise for fresh grapes and dried grapes—on each of them two sets of lashes. But since one is not lashed for a general prohibition, he is only liable for each of those mentioned under one prohibition. Likewise they said, “Do not eat from it raw or cooked”; it is as if it had said, “Do not eat from it except roasted.” If one ate it raw, he is not liable twice, once for raw and once for “do not eat it except roasted,” because this second prohibition is only inferred and is a general prohibition. But he is liable to one set of lashes for raw and one set for cooked. Understand this matter well, for it is the hardest of them all. Also in this category, if one prohibition includes two or three forbidden acts, such as “Do not eat over the blood,” this prohibition includes many things. We learn from it: do not eat from an animal before its life departs. We also learn from it: do not eat from sacrificial meat while the blood is still in the basin, that is, before the blood has been dashed on the altar. We also learn from it: one does not hold the meal of consolation for those executed by the court. We also learn from it: the court does not eat on the day it executes a person. The language of the Talmud regarding all these prohibitions is: one is not lashed for any of them, because it is a general prohibition—that is, it includes many prohibitions, and none of them is explicit, such that we could say one is lashed for the one that was specified, one set of lashes, in the way we said regarding the new crop and Passover. This is clear and easier to understand than the previous examples.

Maimonides’ position in the second root is that anything not explicit in the Torah—including expositions and laws given to Moses at Sinai—is rabbinic law, and therefore one is not lashed for it. So the first two examples are not evidence for our issue (in idolatry this is apparently some kind of exposition, and in slaughtering this is a law given to Moses at Sinai; and in my book Ruach Mishpat I discussed at length that according to Maimonides, a doubt about a law given to Moses at Sinai is ruled leniently).

As for the example from tractate Makkot: in such a case we are dealing with a prohibition inferred from a positive commandment, which is therefore a positive commandment, so one is not lashed for it. That is not because it is not explicit, but because it is not formulated explicitly as a prohibition. And regarding a general prohibition, he discussed this at length in the second part of the ninth root, and there it seems he does not mean that this is because it is not explicit in the Torah, but because there is no formal warning attached to it. To administer lashes you need a warning.

In general, I think no proof can be brought from Maimonides to our discussion, because his view regarding Torah-level and rabbinic law is very unusual (and I discussed this at length in my book Ruach Mishpat).