Some what. In a vector space, we have the 0 vector as well as the condition that if u and v are in the space then u+ v and av, for v any scalar, are in the space. An "affine" space doesn't have that property but- given any affine space, if u and v are in the space then there exist a vector, w, such u= w+ x, v= w+ y, x+ y+ w is in the affine space, ax+ w is in the space, and at+ w is in the space.

Geometrically, you can think of a one dimensional vector space as a line through the origin or a two dimensional vector space as a plane through the origin in three space. You can think of an "affine" space as a line or plane that does NOT contain the origin.