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!