Static comes from the same root as stasis, meaning stop, immovable,
To create static electricity, you have to rub two different materials. At the moment you rub them, the electrons already moved
Note the word "create", creation is not static, and yes there are transient fields and currents during creation of a static field. The static describes the situation after the creation of the field. This will be static because it will not change unless energy is inputted in some form, motion or current. The description is geometrical for static electricity, and geometry is unchangeable, unless some energy input changes it and generates new geometrical patterns. Mathematically it means that in the formulas for static fields there is no functional dependence on time.