Gemara

61a (Mishnah - Chachamim): A Zonah is only a convert, a freed slave, or one who had Bi'as Zenus.

68a (Beraisa): The following disqualify a Bas Kohen, Bas Levi or Bas Yisrael through Bi'ah: a nine-year old Kusi, Nasin, Chalal, Mamzer, or converted Amoni, Mo'avi, Mitrzi or Edomi.

(Rav Yehudah): We learn from "U'Vas Kohen Ki Sihyeh l'Ish Zar" - once she has Bi'ah with a man forbidden to her, he disqualifies her.

Objection: That verse teaches that marriage to a Zar forbids her to eat!

Answer: That is learned from "She will return... she will eat the bread of her father's house". "Return" implies that before (being widowed or divorced from the Yisrael) she could not eat.

Question: This teaches that such men disqualify a Bas Kohen. What is the source that they disqualify a Bas Levi and a Bas Yisrael?

Answer: We learn like R. Aba taught (elsewhere), from the extra 'Vov' in "U'Vas".

Question: This teaches that they become forbidden to eat Terumah. What is the source that they become forbidden to Kehunah?

Answer: We learn from a Kal v'Chomer from a divorcee. A divorcee may eat Terumah, but is forbidden to Kohanim. All the more so, one who may not eat Terumah is forbidden to Kohanim!

Question: (What is the source that all the men in the Beraisa disqualify?) Perhaps Bi'ah only of Chayavei Krisos disqualifies!

Answer: "Ki Sihyeh" connotes Kidushin. There cannot be Kidushin with Chayavei Krisos.

A Nochri or slave disqualifies due to R. Yishmael's teaching:

(R. Yishmael): "A Bas Kohen who was widowed or divorced... (returns to eat Terumah)" applies to men from whom she can be widowed or divorced. A Nochri or slave permanently disqualifies her.

Suggestion: Perhaps even Machazir Gerushaso (after she married someone else) disqualifies her!

Rejection: "L'Ish Zar" connotes one who is foreign (forbidden) to her from birth.

Question: If so, a Chalal, who is permitted to her, should not disqualify her!

Answer: "(A Kohen Gadol) will not disqualify his seed..." equates his (Pasul) seed (a Chalal) to him:

Just like he disqualifies, also his seed disqualifies.

Yevamos 84a: If a Chalal had Nisu'in with a Kesherah, he made her a Chalalah.

Kidushin 77b - Question (Rav Papa): If a Yisrael had Bi'ah with his sister; this makes her a Zonah. Does it also make her a Chalalah?

Answer (Abaye): A Chalalah comes only from Isurim of Kehunah.

Rishonim

Rif and Rosh (23a and 7:5): The following disqualify a Bas Kohen, Bas Levi or Bas Yisrael through Bi'ah: a nine-year old Kusi, Nasin, Chalal, Mamzer, or converted Amoni, Mo'avi, Mitrzi or Edomi.

Rosh (6:6): Chachamim say that a Zonah is only a convert, freed slave, or one who had Bi'as Zenus. This refers to Chayavei Kerisos, in which there cannot be Kidushin, or a Nochri or slave. Chayavei Lavin in which there can be Kidushin does not make a Zonah.

Rambam (Hilchos Isurei Bi'ah 18:1): If a woman had Bi'ah with a man forbidden to her by an Isur that applies to everyone, or with a Chalal, even though she may marry him, she becomes a Zonah.

Rebuttal (Ra'avad): These rules are wrong. A Zonah results only from Chayavei Kerisos or a Nochri or slave, who cannot have Kidushin. However, if any Pasul had Bi'ah with a girl he disqualified her from Kehunah and Terumah. Even a Chalal disqualifies. "V'Lo Yechalel Zar'o" equates his children to him. Just like he is Mechalel, also his children. However, there are no lashes for Zonah.

Defense #1 (Migdal Oz): The Halachah follows all of the opinions in the Beraisa about what makes a Zonah, except for R. Yehudah and R. Elazar. It is clear from many Sugyos that all Pesulim forbid to Kehunah.

Defense #2 (Magid Mishneh): We learned (Yevamos 68a) that all Pesulim forbid to Kehunah, and that Zonah comes from Chayavei Kerisos (Kidushin 77b).

Question (Beis Yosef EH 6 DH veha'Rif): How can the Ra'avad, Tosfos and Rosh say that Chayavei Lavin do not make a Zonah? The Rosh himself brings the Beraisa that says that they forbid to Kehunah, and surely this is due to Zonah!

Note: The Migdal Oz assumes that Pesulim disqualify like Chachamim say, due to Zonah. The Magid Mishneh assumes that all the Pesulim forbid her the same way. Alternatively, the Gemara says that the Kal va'Chomer does not Mechadesh the Isur to Kohanim. Rather, it is a Giluy Milsa. I.e. it reveals that the Isur caused by Bi'ah of a Pasul is already known elsewhere. The Torah forbids to Kohanim only a divorcee, Chalalah and Zonah. We know that Pesulim that are not Isurei Kehunah cannot make her a Chalalah, so they must make her a Zonah!

Answer #1 (Bach DH Eizo): All agree that she is forbidden to Kohanim. The Ra'avad, Tosfos and Rosh say only that she is not a Zonah, so she is not lashed. Rashi (68b DH Giluy) explains that the Kal va'Chomer reveals that the Isur "U'Vas Kohen..." is not only to Terumah; it is to Kedushas Kehunah.

Answer #2 (Beis Shmuel 16): All agree that she is a Zonah. However, we learn that she is forbidden to Kohanim through a Kal va'Chomer, so we cannot lash for this. We said that it is a mere Giluy Milsa. Abaye and Rava (Sanhedrin 54a) argue about whether or not one is lashed in such a case. The Ra'avad, Tosfos and Rosh rule like Rava, who says that he is not lashed. I do not understand why the Rambam obligates lashes

Note: Lishkas ha'Sofrim (in Rosh Pinah Shulchan Aruch) answers based on the Magid Mishneh (Ma'achalos Asuros 2:1). When the Torah explicitly forbids something Michlal an Aseh, we can lash for it if a Kal va'Chomer teaches a Lav. He does not explain which Aseh forbids a Zonah to a Kohen.

Magid Mishneh: Perhaps the Ra'avad calls a Chalal 'Isur Kehunah' (and he makes a Chalalah), even though it is Bi'as Heter, because he results from an Isur Kehunah.

Sha'ar ha'Melech (24) and R. Akiva Eiger: The Gemara (Yevamos 84a) explicitly says that a Chalal makes a woman a Chalalah through Bi'ah!

Rambam (3): If a Nochri, slave, Nasin, Mamzer, converted Amoni or Mo'avi or first or second generation Mitzri or Edomi, Petzu'a Daka, Krus Shofchah or Chalal had Bi'ah with a Yisraelis she becomes a Zonah.

Poskim

Shulchan Aruch (EH 6:8): Any woman who had Bi'ah with a Chalal or a man forbidden to her by an Isur ha'Shavah b'Chol becomes a Zonah... Some say that Chayavei Aseh or Chayavei Lavin, even of kin, do not make a Zonah.

Question (Chelkas Mechokek): I do not know why the Shulchan Aruch brought this latter opinion. All agree that they forbid her. They argue only about lashes for Zonah, and nowadays we do not lash!

Answer (Gra 23): According to Tosfos, even from Chayavei Lavin the child becomes a Chalal (from a Kal va'Chomer from a widow to a Kohen Gadol) if and only if she becomes a Zonah. The Rambam holds that the child is not a Chalal even from Chayavei Kerisos. Indeed, Chalalim and Chalalos are only from Isurei Kehunah. However, in any case a daughter (Leah) of Pesulim is forbidden to Kehunah (from the Kal va'Chomer). If Chalal is only from Isurei Kehunah mentioned in the Torah, the latter opinion is Machshir Leah's children from a Kohen. However, 'Chalal is only from Isurei Kehunah' connotes even those not explicit in the Torah. If so, the Shulchan Aruch brought the latter opinion needlessly.