5 minutes late to a movie is acceptable, since it's just the exposition. That just late.

2 hours late to a movie is just pointless, since the movie's probably finished by now. That's too late.

nah you could be late, but not miss youre opportunity. if youre too late then not only are you late but the thing you came for has now passed. having to rather than too should count as a typo tho >:(

I think too late implies you missed out. I was late to the meeting vs. I was too late to buy tickets.

I believe you would say it the same way. The context of the situation would make the meaning clear.