Mom, I completely agree with you. I think we sometimes get sloppy about how we use the terms and generally assume that when someone uses the term spinning they mean a high cadence . One-legged drills are a good example. You can't mash because you couldn't pull up on the pedal, but your cadence is very low. Therefore, technically, you are spinning because your stroke is even.

Here's my take on the definitions --

Mashing = only pushing down on the pedals

Spinning = Probably best described by Greg LeMond as driving forward with your knee across the top of the stroke and wiping goo off the bottom of your foot across the bottom of the stroke. It is very difficult to get a good spinning motion without clipless pedals.

Cadence - the speed at which your cranks/pedals are rotating.