Confusing words – see / watch

A question on the forums asked about the difference between see and watch.

—Do you often_____ a movie?
—No, I often______ TV.

I chose "watch" for both, although you can also "see something on TV", or "see a film".

"Watch" is normally used when we look at something with attention, while "see" often refers to our ability to see.

"I love to watch the sunrise from my window."
"I can see the mountains in the distance."

But when you refer to habit, I think "watch" is the better word, as you are deliberately choosing to watch something with attention. My dictionary gives the example, "After I finish my homework, I usually watch TV."

What do you think?