Holding NCAA and/or NFL "Philosophies" aside for the moment, there is some clarification built into existing NFHS Rules regarding "Catch" and (Player) "Possession" worth considering. "Catch" (NF: 2-4-1) speaks to "the act of establishing player possession"..."and first contacting the ground inbounds while maintaing possession of the ball".
NF: 2-34-1 advises, "a ball is in player possession is a live ball held or controlled by a player.....after he has caught or recovered it".
As suggested above, a judgment is required to determine whether a player actually does "hold" or "control" a ball (passed to him) and if that holding or controling is established when the player is airborne, he is required to maintain it when, "first contacting the ground inbounds".
There are 3 basic levels of football rules, for good and practical reasons, (NFHS, which includes most Youth level, NCAA, collegiate and MA and TX HS and NFL, professional) and sometimes "philosophies" created at one level can be helpful in establishing judgment criteria, at other levels, but not to the extent they contradict, or expand beyond the intent, rules at other levels
If the judgment of the covering official is that a catch was completed, and subsequent loss of possession is either loss of a dead ball, or a fumble. If the judgment is that a catch was NOT completed, the pass is incomplete or subsequently caught or someone else catching, or intercepting, it.