There is some overlap between them, in the meaning "maybe, possibly, conceivably." That's what fortasse means; and forte sometimes is used that way, as well. (So, a person is making a guess about the meaning of something: Fortasse sunt ebrii, Maybe they're drunk--and that's why they're so disorderly.)
But forte has a lot more going on! It's a narrative device to signal "a chance event or circumstance" (quoting the OLD): "As it so happened," "as luck would have it." It can mean "at random, by chance, accidentally, fortuitously." (Forte psittaci erant ebrii: "As it happened, the parrots were drunk, and that's why robbers stole all the gems...")
They are synonymous in the sense of perhaps.
Fortasse also means possibly, and forte also means perchance.
Furthermore, forte has a some other meanings, such as accidentally and once upon a time.
As a noun forte is the ablative of fors, luck, and as an adjective it means strong, from fortis.