As I understand it, the movie was originally supposed to be The Revenge of Khan, but the upcoming next Star Wars film was (falsely) believed to be titled The Revenge of the Jedi, so the Star Trek movie was renamed.I've never heard that before. But either way, The Wrath of Khan was very clearly a sequel to Star Trek: The Motion Picture, whereas Star Trek (2009) very clearly is not.Wasn't Star Trek II: The Wrath of Khan, originally, Star Trek: The Wrath of Khan?
If anything, The Wraith of Khan was a sequel to the TOS episode Space Seed and not The Motion Picture. In terms of style, action adventure, TWoK was more closely tied to the series.
It used the same sets, the same models, the same actors, the same characters, and it followed up on developments made in TMP. And it whatever its early title might have been, it was, at the end of the day, called Star Trek II.
It was a sequel to Star Trek: The Motion Picture.
Star Trek Eleven is far more a sequel to it's immediate predecessor Star Trek Nemesis, consider ...
You've pointed out parallels in their stories, not identified ways in which one story directly followed up on the other. At the end of the day, Star Trek (2009) is no more a sequel to Star Trek: Nemesis just because both involve Romulans with big ships than Batman Begins is a sequel to Batman & Robin just because both involve Batman saving Gotham City.