UF Honors, Does applying for it mean you have to go to UF?

Common sense tells me no, but can I get confirmation?

No.
If you apply to UF, are accepted and have the required stats you will be invited to the Honor’s program You do not have to go into the Honor’s program (but I have no idea why you wouldn’t accept). If you do not get into Honors the first go round as an entering freshman you may apply for Honors after the first semester.

Of course not. No one can make you go to UF.