Indeed. That's why I think it might have made sense back in Ampere's time. The classification of these regimes (electrostatic, magnetostatic, electrodynamic) is more recent, and Ampere's own theory of electrodynamics deals more with what we term "magnetostatic" today.
I suspect that it corresponds to Newtonian Statics, the study of mass and forces. It's a subject area; an ignoring of changes. Not a state of nonmoving. The Newtonian Statics viewpoint involves summation of forces. It may also involve taking a snapshot at one point in time.
E.g., when a mass above Earth is in free fall, it still obeys Newtonian Statics: the weight/attraction force, easily analyzed from moment to moment. The resulting acceleration and trajectory then falls under "Dynamics."
In other words, electrostatics applies to capacitors and to the mechanical forces produced by electric fields. Even if currents are also present, and even if the e-fields are changing with time, electroSTATICS still applies. (A high voltage, high-amperes power line is very "electrostatic," because of the significant e-fields and resulting phenomena.)
Static Electricity then is a chapter title, with no existence in the real world. Neither can we fill a box with Newtonian Statics. To be consistent, we wouldn't say "electrostatic motor," instead call it a capacitor-motor, or an e-field motor. (Heh, a stretched spring is statically charged! Full of Newtonian-static energy!)
