(Not a Teacher)
"Have" and "got" can both be used to denote possession (they often come together, in fact):
"He has a bad case of the flu." --- "He has got a bad case of the flu."
"He has an Audi." --- "He has got an Audi."
You may also hear it in the future tense, though not as often because it sounds a bit more verbose (though it's only one extra syllable):
"He will have enough money to rent an apartment." --- "He will have gotten enough money to rent an apartment."
However, you don't really see "got" used this way in the past tense:
You can say, "He had a drinking problem," but "He had got a drinking problem," is incorrect.
They're also used to convey obligation:
"You have to go to the family reunion." --- "You have got to go the family reunion."
"Get" has additional meanings of "to obtain, retrieve, or receive":
"Martha, would you get the flour out of the pantry, please?"
"She got the utility bill in the mail yesterday."
As well as some other harder to pin down meanings:
"Hey, could you get the lights on your way out?"
"He got a little cantankerous after a few Tequila shots."
"I'm getting hungry."
"They got married under the Eiffel Tower."
I hope this is at least somewhat helpful.
Student or Learner