Hi Jorge, that's a great question! I would say "have someone do something" and "get someone do something" are very similar in that the end result is the same (someone will do what you told them to). However, I do see a little difference between the two.
To me, if you have someone do something it just means that someone will do what you ask them to do, it's like you're giving them a task.
When you say that you got someone to do something, you might be stressing that you had to convince someone to do something that they were not necessarily very willing to do. Sometimes, this can sound like they did you a favor.
Look at the sentences below:
1. I had my brother drive me around all afternoon
2. I got my brother to drive me around all afternoon
To me, sentence 1 could be rephrased as "I made my brother drive me around all afternoon" while sentence 2 would be "I convinced my brother to drive me around all afternoon." Now that is, if you're being very specific. But when speaking, I would say people can use them interchangeably. You could just be focusing on the end result and say sentence 1 when in fact you did have to persuade your brother -- you might just not be stressing that part.