Several species-specific languages - standard Elvish (as opposed to any of the many dialects), standard Dwarvish, Hobgoblin, and a couple of others - are pretty much the same across all worlds largely because the associated deities gently keep them that way.
Some quasi-universal Human languages - Greek, Norse, Celtic, some others - work similarly, and for the same reason. Other more local languages might only exist in a very small region of one world.
Common, on the other hand, is somewhat world-specific. Yes it's comprised of borrowings from the other languages, but exactly what it borrows from who tends to be different world by world; thus someone from world A might understand one or two words in ten of the Common spoken by someone from world B but be more or less able to converse in Common with someone from world C.
Language barriers are very much a thing in my game. Nobody ever has Common as their native tongue (i.e. what they grew up speaking), and there's no baked-in requirement that players choose Common as one of their PC's languages; thus situations where two or more members of the same party don't share any languages arise on a fairly regular basis. Needless to say, perhaps, magic items that provide translation are quite sought-after.
Edit to add: as with
@el-remmen , characters are not assumed to be literate in my game unless they are arcane casters (who by default have to be literate in something in order to write in and read from their spellbooks!). Even arcanists are only automatically literate in their native tongue; for al other languages and for any language known by a non-caster, literacy in each language known that has a written form* is determined by random roll based on class and intelligence.
* - a great many "monster" languages don't have a written form as the entire species is essentially illiterate or, in the case of some, physically incapable of writing.