What is the difference in notation between $GL(V)$ and $\mathcal{L}(V)$

Question

I know it is a very simple question but I thought it would be useful for more people, since it is kind of confusing because of the similarity of the notation. From wikipedia, I was given that $GL(V)$ represents the group of isomorphisms that are biyective, while I know by myself that when written $f\in\mathcal{L}(V)$, it means that $f: V\rightarrow V$. Is the difference between both that $GL(V)$ is a group while $\mathcal{L}(V)$ is a set? Added into the fact that $f\in \mathcal{L}(V)$ doesn't necessarily need to be biyective, isn't it?