There's no difference in meaning, but it's usually more informal to say you "got" something done than to say you "had" something done. Sometimes one or the other is more commonly used to describe specific actions, but it would never be incorrect to use the less common one. Most people would say they "got" their hair cut; but if you said you "had" your hair cut, everyone would know what you mean.

The difference is that the first sentence is a respectable one, whereas the second sentence is a lazy one. The verb "get" means almost whatever the speaker wants it to mean. In this case "got" means "had", because that is what the speaker wants it to mean. The lesson of the story is: Be clear, don't rely on the verb "to get".

Note that ‘had’ is more precise if you are talking about someone else doing it. Example of ‘get’ with a different meaning: A: What have you accomplished this evening? B: I got my history homework done. Here we’d assume that B did his own homework. B could have alternatively said ‘I finished my history homework’ or simply ‘I did my history homework’ but ‘getting something done’ is common and understood.

Jonathan is right. I have a hard time explaining the difference to my students. Got, in my felling, is more British than had, too. Just a thought!