One thing about cover songs is that there are a lot of weird edge cases. And so people ask What does your account say about… some oddity that they have in mind. For example: What does your account say about Tom McGovern’s video where he plays John Melloncamp’s “Jack and Diane” but replaces the usual lyrics with permutations of the phrase “suckin’ on a chili dog”?
The answer is a bit convoluted.
In live performances, Chris Cornell would play the tune to U2’s “One” while singing the lyrics to Metallica’s “One.” Rick Beato includes it on his list of the best cover songs ever, but one might be hesitant to call it a cover. I know some people who would call this a mashup, but I’m not sure whether that’s common usage either. Mashups are often understood to be digital manipulations that combine elements from different tracks. For example, here’s the definition from r/mashup: “A mashup is a song or composition created by blending two or more pre-recorded songs, usually by overlaying the vocal track of one song seamlessly over the instrumental track of another.”
To keep these straight, we might say that the digital kind of thing that appears in r/mashup’s definition is a mashup remix. And we might call a performance like Cornell’s, which sets the text of one song to the tune of another, a mashup cover. That keeps the distinction straight with just a little bit of extra jargon.
The kind of mashup given as the usual case in r/mashup’s definition is often called an A-vs-B mashup, because it combines parts of one song A with parts of another song B. Although I’ve never seen the phrase used, the formula suggests the possibility of an A-vs-A mashup— one which combines parts of one song with itself.
So McGovern’s video, put concisely, is an A-vs-A mashup cover.

The old term “interpolation” may be of use here.
Interpolation is a much broader category which includes things like quotation, where snippets of an earlier song are set in a new musical context. So while the Chili Dog Song is an interpolation, it’s more than just an interpolation.