Yevamos 61b discusses the many shitos regarding who is a zonah.
Rabi Yehuda: an aylonis (a woman who will never have simanim of naarus; she never reaches sexual maturity) is a zonah.
Rabi Eliezer: zonah is literally a zonah (i.e., an unfaithful wife).
Rabi Akiva: mufkeres (available to anyone).
R' Masya ben Charash - he was going to have her drink the mei sotah and he had relations with her (it is prohibited once he decided she will drink before she actually does).
Chachamim: giyores or freed slave or one who had a forbidden be'ilah.
R' Elazar: two unmarried people having relations. (Tosfos s.v. adds even a married man with an unmarried woman.) (See Shita Kesuvos 13a s .v. ela harei zu, from the Likutei Hagaonim that this is only R' Elazar's opinion and it is rejected. The Shita much later on brings a Ritva who says that some amoraim in Sanhedrin follow this opinion.)
I'd like to give some sevaros for these opinions.
Rabi Yehuda might hold when there will be no fulfillment of perya verivya due to the physical inability of the woman to have children, she is a zonah.
Rabi Eliezer understands the word zonah literally, not as a din.
What is the difference between Rabi Akiva and Rabi Elazar? Tosfos Yeshanim say the nafka mina is the first biah: to Rabi Elazar she will become a zonah from the first biah, and to Rabi Akiva she won't become a zonah until the second biah.
R' Masya ben Charash might hold when there is any prohibition, even though it is not arayos (and does not carry the death penalty), it makes her a zonah. See Rashi Bamidbar 5:31 in the davar acher.
Chachamim hold it's someone who had an arayos relationship or anyone not born Jewish. If she is allowed to marry a psul (like a giyores marrying a mamzer) that same woman cannot marry a kohen, because she is a zonah. Or if she had a relationship where the child born would have been a mamzer, that makes her a zonah. (Rabi Shimon ben Gamliel on 60b holds if she converted before age three she may marry a kohen. This would be because she can be examined and if her hymen is intact she is not a zonah, and the hymen will grow back if penetrated before age three.)
Rabi Elazar can hold one of several things. He can hold like the Rambam in Sefer Hamitzvos (L"S 355) that the mitzva of perya verivya is to get married with chuppa and kiddushin. If you violate that, you become a zonah. Or he can hold slightly different, like the Raavad in Shita Mekubetzes Kesuvos 7 (discussed here) and say that one who violates an isur aseh becomes a zonah.
We pasken like Chachamim (and not like Rabi Shimon ben Gamliel about a girl who converted before the age of three. A question I have is what if a pregnant woman converted and then gave birth to a girl, can she marry a kohen? The baby would not require geirus because we say "ubar yerech imo (the fetus is an appendage to the mother)." I'm not positive, but I don't think she can marry a kohen. I think Ramban considers that a geirus on the fetus. So she would be a considered a giores.