have to 和 have got to 都表示客观的“必须”，即有外力（外人）作用下的“不得不”。（主观的是must）
一般情况下，它们可以互换。如：
Sorry, I can't come out now. I've (got) to tidy up my room before I'm allowed out.
He has (got) to attend the clinic every two weeks. He's really quite seriously ill.
区别在于，have got to 属非正式文体，过于口语化，而have to 比较正式。
还有一点，如果有频度副词 （always, often, sometimes,never等）修饰，只能用 have to。如：
3. I usually have to work on Saturdays so I hardly ever go away for the weekend.
4. They sometimes have to get their own suppers if their mother is working late.
（注：以上例子来自BBC英语频道）