Star Trek II will be setting everything up for the movie where ST meets Babylon 5, BSG and Doctor Who.
And then a whiplash propels the Enterprise into a time warp, and flings them across space, until they end up a long time ago in a galaxy far, far away.
Every Star Trek movie over the past 15 years or so has imitated TWOK in some way, even Trek XI. Hell, XI practically masturbates to TWOK. Expect Trek XII to continue this fine tradition.
In some ways (revenge-seeking villain, uber-weapon, character emphasis). But as against that, it was upbeat and optimistic (Vulcan's destruction aside) and ended on a happy note (albeit that there was some hope at the end of TWOK). The themes of ageing, mistakes of youth returning to haunt one were absent from ST09 - mainly because it was about a group of young people.
Yes, but, they weren't shy about "paying tribute" to TWOK. Things like:
-The Ceti Eel.
-The Kobyashi Maru having the exact same sound effects.
-"I have been and always shall be your friend."
-Not only was there a revenge seeking villain, he was seeking revenge over the loss of his home, and "beloved wife."
I could go on, but I've made my point.
Those are all very superficial items. Those Easter Eggs don't have much to do with themes and tone of ST09, which were very different than TWoK.
As Captaindemotion pointed out, the themes of TWok revolved around aging, facing ones past (which goes hand-in-hand with aging), and revenge (in this film, the revenge went hand-in-hand with facing ones past).
I'll give you that both films had an antagonist who was bent of revenge, but that's hardly an original theme. Revenge is an extremely common motivation for the antagonist in many stories, and I'm not sure you can say that ST09 got the idea to use that theme from TWoK.
TWoK's major theme was not really Khan's revenge -- that was almost a side story/diversion to the main theme of the film. The main theme of TWoK was the main protagonist's (Kirk's) theme, which was extremely front-and-center throughout the entire film was about
finding ones place in the world as one ages, and all of the things that go along with aging -- such as losing friends and family, and coming face-to-face with the the ghosts of the past (those ghosts would be Khan AND Carol/David).
That theme was obvious and right up front in the 2nd scene of the film -- the scene with Kirk and McCoy in Kirk's quarters/apartment. That was the key scene in the film that set up the themes and tone for everything that followed. The themes and tones conceived in that TWoK scene were not the same kind of themes in ST09.
If you want to be
slightly superficial, you could say TWoK's theme was about Khan's revenge. I suppose Nero's revenge is similar -- I'll give you that, like I said before. But I never felt that Khan's revenge was the main theme of the film.
If you want to go
really superficial, you can talk about Ceti Eels and such. Yeah -- both films had them, but that's more of an in-universe cross-film reference that is done all the time in Star Trek films, not just ST09.