Think of a pendulum. It has good static stability in that, when displaced from neutral and then released, it will try to return to neutral. Problem is that it will then overshoot to the opposite side by nearly as much as the first displacement, before swinging back again.
So the pendulum is statically stable, but its dynamic stability is roughly neutral. If some kind of damper is fitted, it will retain its static stability and gain some dynamic stability.
Now think of a pencil standing vertically upright on a flat, horizontal surface. When the top of it is displaced slightly, it will try to return to the vertical, but will overshoot. Chances are it may topple over altogether. In that case it could be described as statically stable but dynamically unstable.
No doubt others will think of some better examples!