I'm not sure it's the same reason for everyone, but my distinction is based mostly on feel. Some days, I'm just hitting them great with my player, and I don't even think twice to pull my jump cue out of the bag. Other days, I'm not confident enough in my stroke to jump with a full cue.
That being said, I feel more accurate with my player, and I can follow, draw, and spin better with my player. (mostly because it's a leather tip vs. g10 on my jumper.)
Some people just can't jump with a full cue as well. With a full cue, weight can be a determining factor as well. Some people play with war birds, 21oz+ tough to jump with that, IMO. Some people play very light cues, 16oz or less. A LOT easier to jump with that.
Keith Hanssen actually plays with a sneaky pete that weighs 12.9oz. (even has a stainless pin that weighs 1.2oz so could go lighter...) Litterally not a shot on the table he won't try with that thing. It's insane. I don't even know how he plays with it. I can jump like you wouldn't believe with that cue.