A field $K$ is called separably algebraically closed if every separable element of the algebraic closure of $K$ belongs to $K$
In the case when $K$ has characteristic 0, it is separably algebraically closed if and only if it is algebraically closed.
If $K$ has positive characteristic $p$ $K$ is separably algebraically closed if and only if its algebraic closure is a purely inseparable extension of $K$