Have to take issue there.
There is no such thing as "American English" there is only the English language.
There may be variations based on location, with different accents but it is still the English language.
Is there such a thing as an "American Mandarin" language?, or "American French" language?, no, just Mandarin and French languages spoken by Americans, usually very badly.
Free to take issue, however, you are not going to change my position, which is also the position of a very big number of people - the distinction is not something invented by me, it is well attested in both professional and academic contexts.
American English and British English differ by what is considered the correct spelling of a number of words (for those words what is considered correct in American English is not in British English, and viceversa).
While I agree it can be considered a detail, in some contexts, e.g. when someone is evaluating the level of English in an exam or in any other formal context (even selection of potential employees), it does matter.
I would agree that, at least as far as I remember, it is mostly due to a few letters (just they can appear in a number of words) - however, there are cases where the difference is in the use and even value given to some words, as well as a number of expressions.
The accent when speaking is the smaller distance, and IMO has often the smaller potential impact, on communication, other differences have a bigger potential impact in communication and understanting, though it is not a problem existing only in English.
Incidentally, I will avoid any comments on Mandarin, because I do not know that language, or anyway I do not know enough neither the language nor the Mandarin speaking communities in USA, but about French...
Aside USA citizens or residents trying to learn "official" French from France (for Zorlun and others, laisson tomber les differences entre les "capitalistes" ;-), comme on dit à Lyon, et le reste de la France
), In North America you have Quebec and Louisiana where they even speak in theory French as mother tongue - however, there is a reason why there is a reference to "Louisiana French" or even directly "Cajun", and to "québéquois".
It may be (actually, it is, in principle) based on the French spoken by the (mostly poor) immigrants in the XVII Century, and French-speaking slaves, but Cajun is far from being understandable by a standard French speaker.
For Québec the situation is "better", meaning the formal language is indeed understandable by European French speakers, and they can be understood without problems in Québec, and is listed a French.
However, it is sufficient to see few phrases to notice things that are "English transposed in French" and that in other French-speaking countries would be considered wrong.
And "real" québéquois is basically impossible for French speakers from other countries to understand, so much that a Canadian movie that was a big success in French speaking countries and not only, even in French-speaking countries in Europe had to have the subtitles in French - maybe for a Canadian from Quebec would have been a funny local dialect but still understandable, but for other French mother tongue, was not understandable.
I spare you the reference to the some other languages.
In Europe we are more used to the idea that there is a language with an official name, but different countries where it is officially spoken over time have developed differences, which mean the official label is one, but the language speakers themselves will recognise variants that are recognisably different, especially by mother tongue (but not only), even if linked, and it is not only a matter of "ex colonies".
