The differences between AMS research journals The American Mathematical Society (AMS) has quite a few journals titled "(something) of the AMS".

The research journals include:


Journal of the AMS
Proceedings of the AMS
Transactions of the AMS
Memoirs of the AMS


How do these journals differ in terms of scope?

Some information about the roles of these journals can be found on the AMS journals website. However the only distinctions given are that JAMS is for "research articles of the highest quality," while PAMS, TAMS, and MAMS are for short, medium, and long articles respectively.

Are there further differentiations between these journals? If a mathematician wants to submit a paper to an AMS journal is the decision process for which one really as simple as "If my paper isn't good enough for JAMS I'll check its length and ship it off to the appropriate one of the other 3?"
If a mathematician wants to submit a paper to an AMS journal is the decision process for which one really as simple as "If my paper isn't good enough for JAMS I'll check its length and ship it off to the appropriate one of the other 3?"


Yes, more or less.  Journal of the AMS is a special case (as you observed) because of its extremely high level, and Memoirs of the AMS because it will consider incredibly long papers.  In both cases, there are only a small number of competing journals with these properties.  On the other hand, Transactions and Proceedings have substantially more competitors.  The primary distinction between them is length, but from my perspective there's also a difference in prestige.  Proceedings of the AMS gets some great submissions, but the length cut-off is pretty short for mathematics papers and this means it gets fewer great submissions than Transactions does, so the prestige level is a little lower.  Other than length and prestige, they are pretty much identical, for example in topics covered (a broad spectrum of pure mathematics, but limited coverage of applied mathematics).

So for Proceedings/Transactions papers, there's a four step decision procedure:


Is your paper on an appropriate topic?  (To a first approximation: is it pure mathematics?)
How long is your paper?
Do you have a realistic shot at acceptance?
Is the journal prestigious enough that you would be happy publishing your paper there?