Before us is Mishnah 2 in Chapter 11 of Tractate Zevachim. The foundation of this mishnah is that the obligation to wash a garment upon which the blood of a chatas has splashed is limited specifically to blood that, at the time it splashed, was fit to be placed on the altar. It does not apply to blood that was already invalidated from being placed on the altar at the time of the splash. The invalidated blood is divided into two subcategories, and the mishnah teaches that even though it lists two, there is no practical difference between them: in both cases, since it involves invalidated blood, it does not require washing in the Temple courtyard.
If so, why does the mishnah distinguish between the two subcategories if there is no practical difference between them, and it seems to be a distinction without a halachic consequence? The answer is that there are two separate exclusions in the verse - two derivations and two different words - each of which excludes one subcategory from the obligation to be washed in the Temple courtyard, and therefore the mishnah mentions both of them separately.
The two exclusions in the verse:
"Hakohen hamchatei osah osah yochalennah" - The kohen who performs the chatas shall eat it. The word "osah" (it) is restrictive and comes to exclude (it, and not another), as it is completely superfluous: the verse could have said "the kohen who performs [the chatas] shall eat," and since it is written, it comes to exclude a specific thing.
"Va'asher yizzeh middamah" - The letter mem in "middamah" (from its blood) is always a term of exclusion: some of the blood requires washing, and some of the blood does not require washing. That is, specifically blood that is not invalidated requires washing, whereas invalidated blood does not require washing in the Temple courtyard.
The text of the mishnah:
"Chatas pesulah ein damah taun kibbus, bein shehayah lah she'as hakosher uvein shelo hayah lah she'as hakosher" - An invalidated chatas, its blood does not require washing, whether there was a moment in time when this blood was valid to be placed on the altar, or whether there was not. The main point is that by the moment it splashed on the garment, the blood was no longer valid to be placed on the altar. From here, the mishnah describes the two types of invalidations: invalidations on account of which the blood was never valid for sprinkling, and invalidations where the blood had a window of time of validity, but it expired by the moment in question.
"Eizu hi shehayah lah she'as hakosher? Shellanah veshenitma vesheyatza" - Which is the one that had a period of fitness? That which remained overnight, and that which became tamei, and that which went out:
"Shellanah" - That the blood remained beyond its allotted time. The usual meaning of linah is remaining overnight, but here it is a borrowed term, as already from the time of sunset the blood is no longer fit to be sprinkled on the altar; in this context, the intention is going beyond the allotted time of nightfall, and not to the morning after the night. The blood must be sprinkled on the day it was received, and if it was not sprinkled, it becomes invalidated. This blood had a window of time during which it could have been sprinkled before sunset, but it was not sprinkled; and therefore, if it splashed on the garment after sunset, its time has already passed, and it does not require washing.
"Veshenitma" - The blood, at the time it was received in a ministering vessel, was valid to be placed on the altar, and subsequently it became tamei in one way or another. This refers to a case where the tzitz does not effect acceptance. The tzitz is one of the eight garments of the kohen gadol, a sort of golden band for the head upon which is written "Holy to God," and when it performs its function, tamei blood becomes acceptable and received. It is worth noting that opinions are divided as to whether the tzitz is required to be on the head of the kohen gadol to effect acceptance, or if it is sufficient that the tzitz is not broken. There is also a separate dispute among the Rishonim whether blood that became tamei can be sprinkled on the altar. In any event, the mishnah is dealing with a scenario where the blood cannot be sprinkled on account of its tumah, such as when there is no tzitz; and since at the time of its reception in a ministering vessel it was valid and not tamei, it had a period of fitness, whereas after it became tamei it is no longer fit. Therefore, if it splashed on the garments after it became tamei, its blood does not require washing.
"Vesheyatza" - The invalidation of going out. The blood was received in a ministering vessel properly in the north of the Temple courtyard, but subsequently it was taken outside the Temple courtyard and became invalidated. Even though it had a period of fitness, and for a certain time it could have been sprinkled properly, once it goes outside its boundary, its previous status does not return and there is no possibility of sprinkling it inside.
"Ve'eizu hi shelo hayah lah she'as hakosher?" - And which is the one that did not have a period of fitness?
"Shenishchatah chutz lizmanah vechutz limkomah" - If at the time of the slaughtering, or at the time of the reception of the blood, the kohen had in mind to offer the blood or the emurim after the proper time or outside the proper place, these thoughts invalidate it, just as a thought of "not for its own sake" invalidates. The offering was invalid from the outset, since it was already invalidated at the time of the slaughtering, and therefore this blood never had a moment of validity, and it does not require washing even if it splashed on the garments of the kohen.
"Veshekibbelu pesulin es damah" - If we leave the slaughtering aside, and say that the reception of the blood was done in an invalid manner: the receiver was not a kohen, or he was a kohen but an onen, or tamei, or he was not wearing the priestly garments properly, and so on, the reception is not valid. And since the only time the blood becomes fit to be sprinkled on the altar is after it was received in a ministering vessel in a valid and effective reception, and in these scenarios the reception was not valid, it turns out that the blood never had a moment of validity for the altar.
In summary: Let us return and look at the overall picture. If the blood, at the time it splashed on the garments of the kohen, was already invalid - whether it was fit for sprinkling at some stage or whether it was never fit - it was invalid at the time of the splash, and this blood does not require washing in the Temple courtyard. The two exclusions in the verse, "osah" and "middamah", are what teach these two subcategories, even though the halachah for both of them is the same.