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Sacrifices where the meat was not put on the altar will not have their hides given to the Kohanim. This is called olah ish, a sacrifice that is valid for a person. The hides of sacrifices offered without proper intent were still given to the priests. The hide is given to the kohanim whether it was brought by a man or a woman. The owners keep the hides of the less holy sacrifices and the priest keep those of the most holy sacrifices. In the case of a burnt offering, which is burned completely, the priests acquire its hide - the rabbis ask why they shouldn't receive the hides in all cases. The altar does not change anything for only the meat is burned on the altar.
The Beraisa discusses the source for the law that the Kohanim receive the hides of Korbanos. The Torah explicitly states that the Kohanim receive the hide of a Korban Olah, but it does not mention this law with regard to other Korbanos. Although the Tana'im derive the law for other Korbanos in different ways, they agree that the hides of other Korbanos of Kodshei Kodashim go to the Kohanim. Does this mean that those hides have the same status as the hide of the Korban Olah, or does it mean that the hides of other Kodshei Kodashim are simply considered secondary to the meat of their Korbanos, which is also given to the Kohanim?