Hello, Sara.

A postman is a man who delivers letters, packages, etc. as a job. A postwoman is a female version of one of these.

Mail carrier, letter carrier and mailman (or mail-woman) are all different names for a postman or postwoman. The most common word in America is "mailman", while in the UK, "postman" is mostly used. ("Mail carrier" and "letter carrier" are less common.) But either can be used in both countries. It doesn't matter - the locals will still understand you.

I hope this helped!

Where I live in the U.S. we say mailman or maillady. Letter carrier is more of an industry - specific term.

Wikipedia has a good article on the different titles.