Which is correct not able or unable?

There's no difference in meaning between "unable" and "not able", but they're not quite interchangeable in some situations. One difference that comes to mind is that we can modify the adjective "unable" with an adverb in ways that wouldn't work with the phrase "not able".

What is the difference between unable and able?

As adjectives the difference between able and unable

is that able is (obsolete|passive) easy to use while unable is not able; lacking a certain ability.