For bands I too use the Washington’s axe metaphor. But I call them a “head & handle” band.
I remember it from that comedian/juggler guy whose name escapes me. He was really popular in the mid-eighties, on Carson, Letterman, SNL, HBO Young Comedians etc. He never came up with any new material so he kind of just faded away.
Anyway, he was famous for simultaneously juggling a knife, a meat cleaver and an axe and when he took the axe out he would say that this was the actual axe Washington cut down the cherry tree with, and that it had been in his family for so long that over the years he’s had to replace the head, and the handle.
I’m surprised to hear that others use this analogy too.