I agree with Anna. These words mean the same thing.
Also I agree that "a lot of " is more formal than lots of, or lotsa.
Please keep in mind that lotsa can definitely be heard in different forms of spoken English. It is natural but not written.
A lot of takes longer to say. If you are giving a speech and you want the listener to really pay attention to what comes after a lot of then separating the words makes it longer and so the listener might be more drawn towards what comes next. I will record my voice and give you an example. But again this doesn't change the meaning.