The Glaswegian taxi driver may not consider themself to be speaking a different language but, if speaking to another local and leaving aside pronunciation, they’d use words, phrases and even grammar that’s incomprehensible to someone with no experience with Scots.
I’m a “posh Scot”, raised middle class in Edinburgh so my accent is minimal and thickens up or softens depending on who I’m speaking to. Even for me, there’s a lot of words, phrases and ways of speaking I’ve had to adjust to be consistently understood by American coworkers when over the last 10+ years.