"See" vs "Can see" - ultimate question

Question

When I went to school, I was taught that "to see" = "to understand", but if you want to speak about eye-vision, you should say "can see". For example: I can see a cat on this tree. This would be wrong: I see a cat on this tree.

Is it really wrong? I have a hunch it might be a British-American difference, could someone confirm it? At school we always learn the British version of English. Do British say "I see a cat"? Do Americans say it? Which one is used more often?

I read: "I see" or "I can see" and "I can see someone " vs "I see someone" - but here the answers consider an obvious case where you put stress or not on the ability of seeing. "Can you see it?" vs "Do you see it?" - here they write about how similar are these two forms and that both seem correct. I'd be interested about regional differences, if they exist.

Answer 1

As a native (British) speaker, I would use both interchangeably. For see you could use it to refer to having sight of something:

I see a ship on the water.

You might then choose to use can see non-literally:

I can see that this might cause trouble.

If there is any difference to be sensed in everyday speech, I might suggest that see sounds a little more formal, though not by much. Otherwise, I can't immediately think of examples that wouldn't work interchangeably.