What is the difference between the states of phase equilibrium and metastability?

The main difference is that the metastable state is not a state of equilibrium, but a state of non-equilibrium that is maintained for a long time. A metastable state is when the system approaches equilibrium in a very slow manner.

And on the other hand the phase equilibrium as the name says is a state of equilibrium in which there are more than two phases coexisting.