I've always considered "scale" to refer to a fixed mathematical relationship to another known standard. For instance; the "scales" on your hand wheels may be marked for 0.001" increments but are 0.050" apart, or a scale drawing.
A "rule" is a tool for marking off fixed increments or lines, either using a scale or an actual fixed measurement standard. In the latter case it becomes a "ruler".
Just my take on things. I'm also in electronics and spent much of my career calibrating laboratory equipment. Given all my time dabbling in things "metrological" I can't remember getting into the rule, scale, ruler debate ever. Guess it all seemed fairly obvious at the time.