A rude person is someone who is deliberately disrespectful, crude, rough and insulting.
An impolite person is not polished, does not follow rules of ettiquette, and does not have good manners. For instance, it would be impolite to crowd in front of the line instead of going to the back and waiting your turn. If he uses impolite conversation, he may use dirty words, have a foul vocabulary and will appear to not have good training. The words are similar, but rude is more on purpose, and they know what they are doing.