It has nothing to do with non revs as you are the 'airlines' guest and everything to do with jumpseating as you are the Captain's guest. Nonrev refers to the parent company's employees and families (ramper, gate agent, OCC, pilot.......) riding their own airline or regional on the parent company's flights. Usually no need to check in, although sometimes a pilot may say 'hi' as a courtesy. You are a guest of the company as this is part of your compensation.

Jumpseat is asking for a ride on an offline company (Delta on Hawaiian). Must check in as you are a guest of Captain and they have authority as to if you can ride. Jumpseat also refers to riding the actual jumpseat or F/A jumpseat on your own carrier which in case it is obvious why you 'check in'.