The definitions are ultimately arbitrary because they're just abstractions and the specifics are often more political than scientific.
Most regional variation these days is what's colloquially called an accent: the exact same words, just with slightly different sounds (strictly speaking: the same phonemes produces slightly differently). Sometimes a few idiosyncratic words are mixed in for good measure.
What seems most surprising to me as a German about English is actually that in the UK there seem to be vastly more dialects compared to Germany but each seems to share much more vocabulary and grammar. The differences often entirely consist of pronunciation.
I guess this is because Germany is historically not one country but several: Bavaria really is something entirely different from Swabia, Saxony, Rhineland or Westphalia. It's just in modern times (literally only in the late 20th century) that most German speakers no longer speak their full regional dialects.
That said, "standard" English is simply a matter of definition. In the UK "standard" means RP, in the US it means GA. There's nothing special about these "standard" versions, they're just a specific dialect that is defined as the standard to be used as the official language. They're still dialects, though.
"Language" really just means "spectrum of mutually intelligible dialects". And that definition is already contradictory because not every pair of two languages within the spectrum is as mutually intelligible as any other. And sometimes different "languages" can be somewhat mutually intelligible (e.g. Afrikaans and Dutch) or even asymmetrical (e.g. Dutch speakers understand Afrikaans better than vice versa).
Heck, in everyday conversation it's probably best to always read "language" to mean "dialect". It's just a useful abstraction that mostly leaks too much to be actually useful.