To catch a ball is to possess a ball, and to possess a ball is to possess it. The question is what does it mean to possess a ball? According to this master of the English language, to possess it means to control it.
I would agree with Mr. Webster's assessment. To carry the word relationship a step further, "control" is defined as, "To exercise a directing, restraining or governing influence over". Unfortunately, what none of these definitions relates to is a required duration, that is
until the NFL added their own concept of "surviving the ground", and even that description is in practice, unfortunately, subject to interpretation.
Where either the goal line, or sideline (becoming OOB) is involved that duration is instantaneous; "Break the plane of the goal" or step on the line, the "lights go out" and what happens thereafter happens to a dead ball, immediately. In contrast, "at the 50 yard line" play continues (the lights stay on) and all sorts of things may happen.
NFHS 2-4 requires
ESTABLISHING player possession and
FIRST contacting the ground in bounds (which includes the End Zones)
WHILE maintaining possession of the ball...".
Sounds like, when "a player
ESTABLISHES possession,
FIRST touches the ground in-bounds, while
MAINTAINING possession, we have a
CATCH, what happens
IMMEDIATELY after that depends on whether the ball remains alive, or becomes dead by rule.