What are the benefits of having one versus the other?
Only schools (including school districts) are supposed to be able to become scholastic affiliates. (There may be some non-schools that have gotten in by mistake over the years, though.)
The primary difference these days is that a scholastic affiliate can run a K-12 JTP in-school event for their students, but ALL of the participants in the tournament must be students at that ONE school. (That means a school district cannot use it to run events throughout their district.)
Any affiliate can run a K-3 (Primary JTP) event, the participants do not have to be students at just one school.
OK, so if I’m setting up a new scholastic chess club through my town PAL, which should I choose? Why would I choose a scholastic, if it’s allowed, instead of a regular?
My town’s elementary school is K-4 and the middle school is 5-8. Since the affiliate wouldn’t be through the school system, my guess is that a regular affiliation would be my best bet.
BTW, what’s a JTP?
Do a search on JTP, there have been several threads that explain the Junior Tournament Player program.
I don’t know what ‘PAL’ stands for, so we’re even. 
PAL = Police Athletic League