Isn't borrow-checking a sort of compile-time reference counting? Not what people usually think of when they say "reference counting", but I wonder if it's a good way to think of borrow-checking.
Not really, it doesn't count references in the same way. The borrow checker maintains a set of rules that are more expansive than reference counting. For instance the rule that you may only have one &mut at a time, and no other references as long as &mut is alive. It also has something like linear types with ownership rules, where owned values can be used only once.
Some people make this analogy, but it has so many caveats, and is so far away from what people think about as RC, and has very serious and significant differences, that I don't think it's a useful analogy, personally. I even might go so far as to say "actively harmful." Not totally sure though.
One of the biggest differences in practice between reference counting and GC (or "other forms of GC" if you consider RC a type of GC) is that nodes involved in a cycle will never be freed.
