African American Vernacular English is shortened to a less precise phrase "Black English". Also, Black English is used in a broader sense:
Black English is a term used for both dialects of English and English-based pidgins and creoles, and whose meaning depends considerably upon the context, and particularly the part of the world.
Also mentioned is AAVE is not regional anymore:
Although no longer region-specific, African American Vernacular English, which remains prevalent among African Americans, has a close relationship to Southern varieties of AmE and has greatly influenced everyday speech of many Americans.
I see the usage of "White English" in some technical sources but I couldn't be sure what is actually meant by that. For example, there is the this explanation from Prof. John R. Rickford from Stanford University:
History of AAVE, exploring earlier examples of African American English, and its source in African languages, as well as the controversial question of its possible creole ancestry. Comparison with creole languages currently spoken in the Caribbean and off the S Carolina coast (Gullah) will be undertaken to shed light on this controversy. A more recent issue, which we will also explore, is whether AAVE is currently diverging from Standard English and White Vernacular English.
So, why is there a prevalent usage of Black English or Black English vernaculars but not White English (vernaculars)? (Or maybe not the usage of vernacular but the phrase itself… there are of course other dialects and sociolects spoken by White people or both White and Black)
For example, there are European Americans also but European American Vernacular English is mentioned in a very few sources. Could this be considered as White vernacular English by linguists in a broader sense? Is there any source that talks about this?
Of course this is related with the history of English and American English but maybe someone can shed a light on the specific topic. Also, I would like to keep the topic in linguistic sense (though it is related with races but within linguistic usages).