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?
Usually the Tosfot commentary for a particular masechet was compiled by a particular Tosafist. Based on clues ranging from outright self identification to alignment of particular shitot, rulings, we can identify a large majority of the authors.
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)