so, honestly JCing is a bit of a misnomer. JCing existed before JC shines in the form of JC grabbing and JC usmashing. These two techniques refer to cancelling the jump animation during startup frames with either grab or usmash.
When people started multishining, they called it JC shining because they thought it was the same mechanic in place (canceling jump startup frames with a move, in this case, shine), because of the observable phenomena that Fox/Falco didn't ever appear to leave the ground while multishining. However, this is not the case, we're shining on the first airborne frame and landing before we jump out again, so technically, this is nothing new. The only novel idea about what we can JC shining is doing successive shines on the first airborne frame.
So to answer JPOBS's question, JC shining is the name given to shining in midair on the first airborne frame such that with little (Fox) to no (Falco) delay on your jump out of the shine, you have already landed again. This lets Spacy players use pseudo-grounded shines in situations where they can jump, but could not normally shine (OoS and startup dash frames).