Using this as a jumping-off point, there were also the major gods worshiped pretty much everywhere (Zeus, Hera, etc) and minor nature deities that were more localized (the god of the closest river, nymphs, etc).
Yes, exactly. Which is why I think most of the Olympians (and some Titans) really don't care where their worshippers are, and why I honour the nymphs of the local waters and woods and not those of Greece.