The Kli Chemdah explains that there are two distinct kedushos to kehunah: 1) Kedusha that comes from being connected to the lineage of Aharon; 2) Kedusha that comes from one’s own identity as a kohen. When it comes to avodah, it is one’s own identity as a kohen which counts most. The avodah of a chalal, whose lineage is tainted, b’dieved is acceptable, but the avodah of a ba’al mum, where the blemish is associated with self, is completely unacceptable. The opposite holds true with respect to tumah. Here, the kedusha of lineage is paramount, and therefore a ba’al mum is prohibited from becoming tamei, but someone who is a chalal is not.
It’s a nitpick, but wouldn’t you have expected the terms used to be reversed? I would have though the term “bnei Aharon” stresses lineage as opposed to self, while the opposite is true of the term “kohanim.” But that’s not how they are used. Ramban writes that “bnei Aharon” is used in the context of avodah, which depends on self, while in our parsha the term “kohanim” is added to stress the connection to lineage.
Chasam Sofer raises the more critical question: If the prohibition of tumah relates to the kedusha of “kohanim,” why does the Torah mention the term “bnei Aharon” here at all? He answers derech derush that Chazal derive from the double-language of amira in the parsha the principle of “l’hazhir gedolim al ha’ketanim,” that one must safeguard even children from the issur of tumah. If the Torah uses the term “bnei Aharon” when it talks about the kohanim working with kodshei kodashim in the Mikdash, the term is equally appropriate for discussing how they relate to the greatest kodshei kodashim, their children.
(OK, forget the derashos, what’s the “real” answer? I don’t know. If you see or think of something good, tell me.)