grammar - "I am gonna have to" vs. "I have to"

To put it simply, "I have to" means you currently are required to; "I'm gonna have to" means you will be required to at some point in the future.

As an example, when describing hypothetical situations, one would say "If he does this, I'm gonna have to do this".

By contrast, when describing a past occurrence, one would say "He did this, now I have to do this".