I tried to google both definitions.
For linear span, click http://en.wikipedia.org/wiki/Linear_span
For linear transformation(wiki takes it as linear map), click http://en.wikipedia.org/wiki/Linear_map
It seems that linear transformation is a subset of linear span? Confused by differences between them.
A linear span is a subspace of a vector space. That means it is a subset that is closed under linear combination of its elements.
A linear transformation is a function from one vector space to another that is linear: $$L(\alpha x + \beta y) = \alpha L(x) + \beta L(y)$$