One of the concepts out there is the idea of a "rage to master." This can be with many highly gifted or almost all prodigies or even some more typical kids. Some of us follow one topic for a whle until we feel done with it, then relax until another takes hold.
Yes!! This... exactly. With everything, not just music. The problem with DD, DS and I is that we delve into something too deeply, beyond its practical application, then become completely bored and done with it and reluctant to resurrect it later when it becomes useful or relevant.
My DS learned to play chess a week or so after his 6th birthday and was the only grade 1 student in his school who could. He could beat adults. He's since become bored and stopped playing. Was he a prodigy?
My DD when she was 7 and burning up the piano recital circuit (lol) had(still has) an aptitude that surpassed many (non musical) adults. She also got bored and drifted away from it and has not progressed at a "prodigy rate" despite her early promise. She is lagging in skills because of her weakened interest (and I never played "tiger-mom") Was she a prodigy?
I think the term can be hard to define. To me it encompasses skill and achievement as well as potential, but I could be wrong.