见面 vs 看见 . . . Which would you use?

Many of my students use "It's nice to meet you" as a greeting when they actually mean "It's nice to see you." In English, the two phrases have two clearly distinctive meanings. I'm assuming that they are using a literal translation of "见面." Is there a major difference in how 见面 or 看见 are used in Chinese? I'd like to make the differences in English clear but I want to make sure I am using clear examples in Chinese.

My students aren't English majors (and this year, none of them were undergraduate English majors either!) so subtle distinctions aren't that easy for them to understand.

Thanks.
I guess I'm looking for the best way to explain to my students the difference between "It's nice to meet you" vs "It's nice to see you." There's a very clear difference in English . . . is there a clear difference in Chinese?

In other words, what would the Chinese be for "It's nice to meet you" (first time meeting)?

What would be the Chinese for "It's nice to see you" (used when you see someone on the street as you are out shopping, etc.)?

Asked by Adair - General Chinese - 3 Answers