Yeah, where is the definition $ \mathbf{P=\frac{E}{V}}$ from? It most definitely does not hold for all systems.


There are systems for which $ \mathbf{P}=\frac{2E}{3V}$ and systems for which $ \mathbf{P=\frac{E}{3V}}$ and systems for which $ \mathbf{P=\frac{sE}{3V}}$ where the relation between energy and momentum is $E\propto p^{s}$ (independent of whether boson or fermions are in discussion).


So yes, they are closely related but most definitely aren't one and the same thing.