As the others have said, in America, 'darn' is a softer expletive that 'damn'. Over there, some people would get upset if you said 'damn'. Here, that's less likely, and 'darn' is not used, unless you are trying to sound American.

Damn is a bad word but darn isn't a bad word?

'darn' is a euphemism for `damn'. In short, damn is stronger; darn is softer.

They mean the same thing. Damn is basically a "bad word" so younger people tend to say darn. Either way, you can say both.