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A douchebag is both arrogant and disingenuous, but the term does not denote any particular level of intelligence or lack thereof, nor does it denote any degree of abrasiveness or lack thereof. A douchebag is always unaware that he is a douchebag.
A douche is both arrogant and stupid, but he is neither disingenuous nor abrasive. Due to his stupidity, a douche is always unaware that he is a douche.
An asshole is arrogant, abrasive and smart, but he is not disingenuous. He may be fully aware that he is an asshole and he may take pride in it.
Bill Maher is an asshole.