Is there a categorical name for differences in the spelling of a word when the word keeps the same meaning and the same sound?
In general, spelling variants or alternative spellings.
More specifically, when one is vastly predominate in one form of English, regional spelling variants.
Alternate spellings or spelling variants--I prefer alternate spelling but see notes below for which is more common where. The title of this post lists some British and American variations in spelling.
"Alternate spellings" and "spelling variants" both directly make sense.
These are variant spellings. (Of course, the Commonwealth could have a body that could rule on the matter, based on which the most common pattern the word should follow. But, of course, no one cares about the million of kids who struggle to learn this hideous and flawed spelling system and no one cares to follow spelling rules either! Kids, why don't YOU follow rules? Complete laissez-faire is dangerous in economics and in ... linguisics. When will THEY get it? RULE(s) ... Britania?)