Indeed. There’s English (no qualifier, just ‘English’) as spoken in England, and there are derivative varieties of it, including ‘American English’.
I hasten to add that that’s not a value judgement; I’m not saying ‘English’ is superior or inferior to ‘American English’, or ‘Nigerian English’, etc.
Personally, I wouldn’t speak of ‘British English’ and wouldn’t say that Americans speak English.
Scots goes further than this: it’s a language in its own right, similar to but distinct from English, like the relationship between Danish and Norwegian (as AlexG55) said ).
Including the Scottish Government, the EU and UNESCO. The last UK census dodged the issue, but listed Scots alongside languages that are unambiguously considered languages.
Much like Catalan and Occitan, the people who speak it understand it as a distinct language, but some nationalists from neighboring, much larger, nations have a vested interest in calling it a dialect.
I feel like the relationship must be similar to Danish / Swedish / Norwegian, which are pretty much mutually intelligible spoken and very similar written. Written Scots is actually more different from English than the Scandinavian languages are to each other.
My great-grandparents were originally from Shetland and Orkney and, according to my father, spoke much like this. Apparently, one of the islands we called home is now abandoned except for sheep.
As that article says, forms of a pluricentric language can diverge until they become separate languages (e.g. Hindi and Urdu, both originally standardised registers of Hindustani).
Presumably that’s what happened to English and Scots, Early Scots being essentially identical to (northern) Middle English:
You can claim that you speak English when you learn to say aluminium properly!
At least it’s nowhere near as bad as the attitude of the French, to people from Canada speaking French. Several of my French friends claim that they can barely understand Canadians, and found it embarrassing when they tried to have a conversation in French.
I only got the first bit “Lang may yer lumm reek” because my grandmother used to say it. It means ‘may you live for a very long time’ or literally ‘may your chimney smoke for a very long time’ (because Scotland is so frigging wet and cold you’ll always have the fire going.) The rest of it? Nay idea.
Fun fact: “smoke” is the original sense of the word “reek”, now lost to English (or at least to English as she is spoke in the south of England). It acquired the (originally secondary) meaning of “stink” by analogy, the pong being imagined as rising from the smelly material in the manner of smoke or steam.