Hi , I need clarification about something

Let's say V is a Vector space over the field F

A is a subspace of V, A={v_{1},v_{2},......,v_{n}}

So my question is what is the difference between Span(A) and the subspace A? Isn't it kinda same thing? Span(A) is the linear combination of the vectors of A with the product of arbitrary scalars.

And subspace has axioms such as it is closed under addition and multiplication with scalar, so if there is a vector u that belongs to the Span(A) he belongs to the subspace A as well because A is closed under addition right?

So my questions is is it possible to have a vector u that belongs to Span(A) but not the subspace A={v_{1},v_{2},v_{3},.......,v_{n}}?

I hope my question was clear, thanks!