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I think it's still Adaptational X. A remake is still a derivative work from a source material that involves new incarnations of the characters, whether or not it's a different medium. Ask in Ask The Tropers to be sure.
an adaptation is when a piece of media is translated to a different medium
—No; a live-action movie can be remade as another live-action movie and that IS an adaptation. The Trope you're looking for is still Adaptational Badass (or Adaptational... Whatever, regarding on what's the case).
^^ I did some a year or so back. I can't remember off the top of my head, but I think they may have agreed with me.
^This is the definition of adaptation in the context I'm using: "a movie, television drama, or stage play that has been adapted from a written work, typically a novel."
This is the definition of remake in this context: "a movie or piece of music that has been filmed or recorded again and rereleased."
Neither says a remake is a type of adaptation, so it might be a misconception to think remakes are such.
Are there any tropes that talk about a a character who's characterization is different between the original version and its remake?
For example, in the first version of a movie, a character was meek and helpless throughout. In said movie's remake, which is a movie, too, said meek character takes a level in badass.
I know this isn't Adaptational Badass since an adaptation is when a piece of media is translated to a different medium, and the example has both the original and remake as movies.