By `two vectors exist in a two-dimensional space` are you talking about how two (linearly independent) n dimensional vectors will span a 2d space?
(A) Look at this space. Every point within it can be reached by combining these two vectors.
(B) Look at this space. No point outside it can be reached by combining these two vectors.
Saying that two vectors span a space is claim (A). Saying that the space they span contains them is... much weaker than claim (B), but it's related to claim (B) and not to claim (A).