MAINT: consolidate API

There are some slight variation with method names even though they do very similar things. I think an API audit and possible cleanup/rename is due.
E.g. driving logic: class names should ideally reflect on the module they belong to, thus #1748 , while on the other hand class methods should be generic as it's in the name of the instance what archive they would query, e.g. https://github.com/astropy/astroquery/issues/2363.

Also, some methods have a bit of a variation in their names while they could be called the same. Some examples are in the final review of https://github.com/astropy/astroquery/pull/2797#discussion_r1287472197, but I'm certain there are more examples (and this should be a bit more carefully checked)

Start with the naming examples in issues #1748 and #2363, then read the final review discussion for pull request #2797. Audit class and method names across the astroquery modules, documenting inconsistent patterns before proposing a consolidated naming scheme. Done means the scope and rename decisions are agreed and the affected APIs are consistently updated.

Written by the indexing model from the issue text.