When I was at the RAM (studying singing) in the 1960s, my piano teacher came out with what seemed a strange statement. He said "The ear hears things faster than the hand plays them".
I was a very argumentative young lady, so I said "that's not possible, surely you mean the ear *seems* to hear things faster than the hand plays them? N, he was adamant, and repeated it again slowly, and showed me what he meant. I was rushing some short semiquaver passages, probably little turns or other ornaments, so as to fit them in the time allowed. The result was that they were smudgy. He showed me how I could put my brain into slow motion for a moment and play the pattern quite clearly and neatly, and it would still come out in time. It felt slower, but it sounded just as quick.
I've been thnking a lot about this recently, and in addition to Fred (you'll have to search for that one, it'll take too long to explain now) Mr Palmer is also turning up in my piano lessons with increasing frequency, to good effect.
Is there aa better way of expressing what he was saying, that would make sense to my child pupils? I do tend just to go into Mr Pal;emer voice, which was slow and lugubrious.
I do sometimes say when kids are rushing through a passage with no real regard for the beat, that they're confusing velocity with vitality. Inevitably they reply "wha' ?" so they learn two new words as well as some musicianship!