Where's the difference between $\vDash$ and $\Rightarrow$?

Question

I'm sorry if that question has already been asked.

Sometimes in propositional logic when proving "$\phi \rightarrow \psi$ is a tautology" using truth tables people write $\psi \Rightarrow \phi$.
But isn't that the same as proving $\psi \vDash \phi$ since truth tables are a semantic proof method?
Where's the difference between $\vDash$ and $\Rightarrow$?