But the problem is, we're not attuned enough to distinguish them. Like you can't hear regional accents in a foreign language you can't understand.
I recall reading that 1/ whales had different regional 'voices' when they sing and 2/ birdsong differs even across the span of the UK. So it is quite probable that cats and dogs do.
Though remember, we often interfere with pets breeding (especially pedigrees) by transporting them across large distances, so perhaps they're a bit more mixed up now!
There will be variations on the animals vocalisations, but remember that pet animals don't speak English - they understand it.
Or whatever languge around them / spoken to them.
I remember hearing of a case of a dog adopted from a rescue centre as the owners were emigrating. The new owners couldn't get the dog to do anything at all until someone pointed out that the previous owners were Swedish - and so the new owners had to learn Swedish to get the dog to obey commands........
There are variations in wild bird song depending on what 'works' for the bird in one area, though by and large the species keep to the same content, which is how twitchers can follow sightings.