They're very similar, and often interchangeable. However "bad" is a bit broader: it can bad in an emotional way, or it be bad in an unemotional way. "Nasty" is generally only emotional. Some examples: 1. A bad teacher might be mean to her students, or she might be a very friendly and kind person but just bad at explaining things. A nasty teacher is one who is mean to her students and makes them feel sad or angry. 2. A "bad film" might be offensive, or it might just be boring or confusing A "nasty film" is offensive and angers its viewers (eg. it's insulting to women). 3. "Bad weather" usually means it's unpleasant. However, if you have a hot, totally dry summer, you can go to the beach every day - good for you, but bad for the farmer whose fruits and vegetables die! "Nasty weather" specifically means weather that makes people uncomfortable.

You are correct. When referring to a bad person, a nasty person would say bad things about your mother, cheat during a game, or just call you *nasty* words. This is not someone that you want to be around... It could also refer to someone that you find very unappealing (or disgusting), for example, that person on the bus or subway that has a really bad odor - so strong that makes you want to throw up - could be described as nasty. But, to confuse the subject, I might warn my children to stop being nasty if they are being very rude. Also, you could tell your friend "dude, that's nasty" if he won't stop burping or farting.... Hope that helps!