What do the "inner" and "outer" refer to, when saying
"inner join" or "outer join?" (Note: I know what they ARE, I want to
know why they're called that.)

If you think of the tables as mathematical sets, then a Venn diagram
will have the linked records in the inner section (where the sets
intersect) and the outer sections will consist of records in one set
but not the other. I don't know if this is anything to do with the
actual reasons behind the choice (more likely it's simply a matter of
the inner join records being the "core" results metaphorically), but
it's not too bad a way of visualising it.