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human
What broad distinction can be made in the fields of study between mathematical logic as practiced by mathematicians and philosophical logic as practiced by philosophers?

I understand that they both rely on the same, or at least very similar, foundation, but when I look at mathematicians vs philosophers who work with logic at my university, they almost exclusively publish with other mathematicians or philosophers respectively? Are the differences stylistic or goal oriented? or more abstract?
gpt
>Are the differences stylistic or goal oriented? or more abstract?

Rather goal-oriented. Usually philosophers and mathematicians are interested in different things. Mathematicians are not interested in, say, paraconsistent/relevant/deontic logics, or the problem of absolute generality, or formal theories of truth, because usually there is not much of interest there for mathematicians. Philosophers, on the other hand, are not that interested in proving some obscure fact (like that there exists an upper bound of something) about first-order logic with two variables. And even when mathematicians and philosophers coincide in the object of study, they are interested in different aspects of that object: mathematicians will not use type theory to discuss higher-order metaphysics. This does not mean, of course, that philosophers and mathematicians cannot significantly influence each other, and it can be difficult to determine whether a work is strictly mathematical or philosophical logic (just think about Tarski or Kripke).

>they almost exclusively publish with other mathematicians or philosophers

In addition to the above, this is also largely due to institutional, administrative, and publishing reasons.