Tosafoth were the sons-in-law, grandchildren, and students of Rashi (and their students), and "they" wrote a commentary on the Talmud that is often at odds with Rashi's earlier commentary. Sometimes there are internal disagreements within a single commentary on the passage of Talmud being discussed. Who is the redactor of the various opinions expressed in the commentary of Tosafoth?
Following @Yahu's suggestion, I'll summarize Urbach's analysis of the editors of the tosfot of the different masechtot:
Brachot - An unknown Ashkenazi (Germanic) scholar who personally knew Rabbi Moshe of Evreux, but was probably not his student. The tosfot are mostly based on the writings of Rabbi Yehudah Messer Leon.
Eruvin - A student of Rabbi Yitzchak of Dampierre (the Ritzva), combining a multitude of different tosfot.
Rosh Hashanah - RaSh of Sens.
Taanit - Probably a student of Rabbi Yitzchak of Tresson, mostly based on Rabbi Yitzchak and Rabbi Yitzchak's rabbi, Ri of Melon's teachings.
Mo'ed Katan - Rabbi Shmuel, son of Rabbi Elchanan and grandson of Ri, mostly based on the teachings of Rabbi Yitzchak ben Rabbi Mordechai, student of the Riva, and those of Rabbi Avraham, student of the Rashba.
Yevamot - Rabbi Eliezer of Touques, using a multitude of different sources.
Kiddushin - A student of Rabbi Yitzchak of Evreux, bringing mostly teachings of the rabbis of Evreux.
Gittin - Unknown. Based mostly on tosfot of Touques or those of Rabbi Eliezer of Touques.
Nedarim - A student of Rabbeinu Peretz, based mostly on teachings from Evreux.
Nazir - A student of Rabbeinu Peretz, based mostly on teachings from Evreux.
Sotah - Possibly a student of the rabbis of Speyer, or perhaps he was Rabbi Baruch ben Shmuel of Mainz.
Horayot - An unknown Ashkenazi (Germanic) editor, based mostly on Rabbi Simcha of Speyer.
Menachot - RaSh of Sens with some later edits by his students.
Chullin - A student of Rabbi Aharon of Regensburg, mostly based on Tosfot Touques.
Bechorot - Rabbi Yitzchak, student of Rabbi Baruch. Mostly based on Tosfot Sens.
Erchin - Possibly a student of the son of Rabbi Shmuel, also possibly a student of Rabbi Mordechai Halevi or the Maharam of Rothenburg, based on a variety of sources.
Temurah - A student of Rabbi Shmuel of Evreux and "Maharar", which is likely either Rabbi Mordechai Halevi or the Maharam of Rothenburg.
Kinim - An unknown Ashkenazi (Germanic) editor, based on Ashkenazi (Germanic) sources.
Niddah - An unknown editor, based mostly on Tosfot Touques.
there are many different tosafot on each meseches some of the more famous ones are
- tosafot harosh
- tosafot ri"d
- tosafot rabeinu peretz
- tosafot tuch (most common alongside gemorah )
- tosafot harashb"a meshantz
- tosafot rabbeinu moshe
there may be as many as 20 on any given mesechet
when the gemorah was published they printed whatever tosafot was available, and most commonly used, on each mesechet by itself.(this also has alot to do with the fact books were hand-written so most commonly used was usually the most availiable) usually the most well written, concise, and compact on that mesechet was considered best. there are many instances which some meforshim say 2 different tosafists are printed a just few pages from one another. (theres a quite few such instances in the first few pages of pesachim)