F is onto, or surjective, if every member of S2 appears at least once. For every b in S2 there is a in S1 such that F(a) = b. When describing such a function, an important letter is substituted: Instead of "into", we write: f maps S1 onto S2.
A bijective function is both 1-1 and onto.
A permutation is a bijection from a set S onto itself. When S is finite, this is a rearrangement of the n elements, as expected.