They are similar. One is emphasizing the process that gave you trouble. One is emphasizing that you are in trouble. Example: "I was working on my homework when I got stuck on the second problem." - thing we're going well and then I had a problem. I'm telling you about the process running into a problem. It's unclear if I've solved the problem here or not. "I'm stuck on the second problem." - I'm telling you I'm still stuck on the second problem.

To get stuck is the process of becoming stuck. After you get stuck, you are stuck, meaning that it's your current situation.

Both are the same

Hi would you like to be partners as we can improve our speaking skills by talking with each other?