Do you still maintain the old distinction between watching and seeing video (and live) entertainment?

This question is not about dictionary definitions. It’s about everyday usage.

We used to see a movie (in a theater) but watch television (at home, implicitly). We’d also see a play or a show; that meant going out to the theatre and buying a ticket to attend a live performance.

I’ve heard people speak of watching a movie when they go out to a movie theater, and it sounds jarring to me. Even more so if someone says they’re going to, for example, watch their daughter’s play at school.

When I put a DVD in the player at home, or tune into a streaming channel, I think of that as “watching” a movie, not “seeing” one, even if the movie was originally a theatrical release. Is it the medium of delivery that makes the difference and not the object of viewing?

Has the distinction between the terms been lost? or is the line simply being drawn in a different place?

When someone says, “Do you want to see a movie?” does that automatically mean “Let’s go out” or not?