(Mishnah): The daughter of a male Chalal is forever prohibited to marry a Kohen.

If a Yisrael married a Chalalah, his daughter may marry a Kohen; if a Chalal married a bas Yisrael, his daughter may not marry a Kohen.

R. Yehudah: The daughter of a male convert is like the daughter of a male Chalal.

R. Eliezer ben Yaakov: If a Yisrael married a convert, their daughter may marry a Kohen. If a convert married a bas Yisrael, their daughter may marry a Kohen. But if a convert married a convert, their daughter may not marry a Kohen. The law is the same for converts and freed slaves, even after 10 generations the daughter may not marry a Kohen, unless her mother is a bas Yisrael.

R. Yosi: Even if a convert married a convert, their daughter may marry a Kohen.

(Gemara - Rav Hamnuna citing Rav): (When the Mishnah taught that the daughter of a male Chalal is forever prohibited, it meant) the daughter, the granddaughter, the great-granddaughter etc. for all generations.

R. Yochanan citing R. Yishmael: The pasuk states (Vayikra 21, 15), "(He shall not profane his offspring) among his people'' - just as the pasuk earlier, in reference to the prohibition for a Kohen to become impure, the pasuk states (ibid, pasuk 1), "...each of you should not become impure to a dead person among his people'', which only applies to men and not women; so too the prohibition to profane one's offspring applies to men and not to women.

Question: What is the practical difference between Rav and R. Yochanan?

Answer: If a Kohen had relations with a divorcee and she gave birth to a son and a daughter and the son later had a daughter and the daughter had a daughter- according to Rav, the son, the son's daughter, and the daughter's daughter are prohibited. According to R. Yochanan, the son's daughter is prohibited but the daughter's daughter is permitted.

Question against Rav (our Mishnah): If a Yisrael married a Chalalah, his daughter may marry a Kohen...?

Answer: The Mishnah's case is of a woman who was born Kasher and became a chalalah through relations with a pasul (e.g. a Kohen with a divorcee). However, if this chalalah had a daughter with a Yisrael, the daughter may marry a Kohen. On the other hand, the daughter of a Chalal is forever prohibited. (The reason is that the first chalalah came from a Kasher source but relations made her a chalalah. Nevertheless, if she married a Yisrael, their daughter is Kasher since Chazal say that Yisraelim are like a Mikveh of purification for chalalos. However, when she was born in a non-Kasher way - as her father was a chalal - her daughter from a Yisrael cannot marry a Kohen.)

Question against R. Yochanan (our Mishnah): R. Yehudah says that the daughter of a male convert is like the daughter of a male Chalal (i.e. Pasul). (And just as the daughter of a convert is pasul, so too her daughter is also pasul)...?

Answer: R. Yehudah is (not coming to disagree with the first tana but rather he is) actually coming to add - since he did not say "the daughter of a chalal is like the daughter of a convert''.