It's clear that Mission: Space is not directly themed to MISSION TO MARS, the film. Sinise is not supposed to be the same character, for example.
I think it's also clear that there is some degree of intentional overlap between the ride and the movie. Props, basic storyline, the presence of Sinise (even as a different character).
"Inspired by" rather than "themed to" is a fair distinction, I'd say.