Static:
A static load is time independent. It’s value is constant w.r.t time.
Dynamic:
A dynamic load is time dependent and for which inertial effects cannot be ignored.
Quasi-Static/Pseudo-Static:
A quasi-static/pseudo-static load is time dependent but is “slow” enough such that inertial effects can be ignored. Note that a load quasi-static for a given structure (made of some material) may not be quasi-static for another structure (made of a different material).
Quasi-Dynamic/Pseudo-Dynamic:
In pseudo-dynamic loading, inertia and damping properties are simulated while stiffness properties are acquired from the structure.
Reference:
enggprog.com - Engineering Programs 