As far as I know, both have the same meaning and both are used in British and American English. I've read that "have to" is more common in American English while "have got to" is more common in British English. Moreover, based on what I found, "I have to" seems to be considered more formal than "I have got to" in both BE and AE (I'm not 100% sure about this).

Yes, they have the same meaning, and both are equally common. There are other ways to say it, like "I must do this," or "I need to do this", or the same way but with different spelling, "I've gotta do this". People might tell you that there are differences in the meaning of each one; don't listen to them. The meaning of each can be slightly different depending on the tone of voice, inflection, and context, but the phrases themselves all mean the same thing. :) I hope this helps!

Hi! There are absolutely differences between the modal verbs, and if you want to sound like a native, you need to know them! However, "have to" and "have got to" are practically the same, although "have got to" is a little less formal. I don't think I've ever heard someone under 70 use this construction without the contraction. "I've got to" sounds much more natural than "I have got to". "I've gotta" would be the most casual form of this construction. If I were you, I would stick to "I have to" to avoid seeming too casual, since "I have to" is fine in casual speech.

Combine both Pablo's and Alexander's answers and you'll get the right one.

Jerry, why?