A question about rank/image of a linear transformation

Let $\displaystyle V$ and $\displaystyle W$ be K-vectorial spaces and $\displaystyle T:V\to W$ a linear transformation.

From my notes, we call the rank of $\displaystyle T$ as $\displaystyle R(T)=T(V)=\{ w\in W : \exists v \in V \text{such that } T(v)=w \}$.

And in the exercises I have there is no mention of the rank of a linear transformation. However I've to deal with the image of a linear transformation in the exercises and I've no mention of it in my notes. So my question is "does the rank and the image of a linear transformation is in fact the same thing?".