To be fearful is (1) to be frightened, or (2) to be inclined to anxiety or fear. The word also works as a colloquial adjective meaning to an extreme degree. To be fearsome is to cause fear or to be capable of causing fear. Things that are fearsome make us fearful.
Tens of thousands of people have turned out for the demonstrations despite still being fearful of the notoriously brutal secret police. [Sky News]
They have a fearsome reputation as bloodthirsty limb-biters with a taste for human flesh. [Salon]
He also tried to convince a judge that he was so fearful of his brother John Hillis that he felt compelled to grab a rifle out of his bedroom to protect himself. [AP]
A fearsome storm has spread a smothering shroud of white over nearly half the US. [Sydney Morning Herald]