"That seems like a somewhat different movie" would be
Whereas "I want to see a different movie" would be
So to answer your question directly, yes, "を見たい" means "want to see" -- and you'd use the kanji "見たい", in most general cases. (There's no だ after みたい in this case.)
When you want to say "is like", you'd say "みたい" without a particle in front, and without kanji.
Though "見たい" is the most general kanji for "want to see/look", you can use more specific ones:
"診たい" -- want to examine, as in examine a patient.
"観たい" -- want to watch, as in sightseeing or watching a movie.
"看たい" -- want to look after, as in looking after a patient, from 看病 （かんびょう） -- not too common.