Answer

In the Torah itself, the specific categories of labor are not written explicitly; rather, what is written is the prohibition of labor on the Sabbath. The detailed definition of what counts as labor comes from the Oral Torah—whether from the thirty-nine categories of labor hinted at in the Torah’s own labor, or from the Tabernacle, or from logical inference. See Tosafot and its commentators on Bava Kamma 2a and elsewhere. Therefore, one might have understood that someone who performs several labors would be considered to have had one lapse of awareness, just like someone who performs one labor in several forms. For example, one who performs a primary category and its derivative, while knowing the basic concept of Sabbath, is liable for only one sin-offering. The same is true for one who performs many labors of the same type. Why? Here too, two details of Jewish law escaped him—that the primary category is forbidden and that its derivative is forbidden. Yet the liability is only one sin-offering, because it is one prohibition and is considered one lapse of awareness. With regard to several different categories of labor, the verse introduces the novelty of distinguishing among labors: several different labors are not like a primary category and its derivative. Incidentally, it is possible that even according to the conclusion after the verse, these are still not several lapses of awareness but one lapse of awareness, and it is like different dishes, which divide liability within the same prohibition. In the Ritva on the Mishnah he cites the Rashbam that regarding a menstruant woman and Sabbath labors, the days themselves also divide liability—and not only in a case of inadvertence regarding the Sabbath, as Rashi wrote there, but also in a case of inadvertence regarding the labors.

It seems that the matter depends on the dispute between Rashi and the Ri of Dampierre as to whether the Sabbath labors are thirty-nine different prohibitions—except that they are not counted that way for reasons related to the enumeration of the commandments—or rather different applications of one prohibition.
I understand that the Ritva you cited is from the Talmud on 70a:
"From where do we derive the distinction among labors?" Meaning, that he should be liable for each and every labor when he did them all in one lapse of awareness. And if you ask: why do I need a verse for that? Since the labors are different and distinct from one another, it should be like one who ate forbidden fat and blood in one lapse of awareness, who is liable for two. One may answer, to the contrary: since they all bear the single name 'labor,' and all are prohibited because of 'you shall not do any labor,' it should be like one who ate forbidden fat and forbidden fat in one lapse of awareness, in which case he is liable only once."
He is saying that doing several labors is like eating forbidden fat several times, which is like different dishes, and not a matter of several lapses of awareness. That is exactly what I wrote.

So we learn that there are two possible ways to understand the division into multiple sin-offerings in a case where one knows that today is Sabbath and knows the basic concept of Sabbath, yet performs several labors: (a) the verse teaches that there are several acts of inadvertence here, not just one; (b) this is one act of inadvertence, but there is nevertheless a division into multiple sin-offerings, like different dishes.
The practical conceptual difference is in understanding what the sin-offering comes for: does it come for the inadvertence, or for the transgression on condition that it was done inadvertently? And the difference would be whether the number of sin-offerings corresponds to the number of acts of inadvertence—every lapse of awareness obligates a sin-offering—or whether it corresponds to the number of transgressions, except that acts of inadvertence separate the transgressions from one another. In an article I once wrote, I brought material on this from Afikei Yam, and I suggested a different explanation. The practical difference there relates to how one views a secular Jew who commits transgressions, and causing him to stumble in sin. See my remarks here in the body of the text after note 17, and in note 23 below. (The system truncated my comments there; in the original I elaborated more.)