I don't know what type of "bushing" you do but mine is always is with an eye of putting something on the table, my dogs are always under my control & do as they are told.
Maybe I'm wrong but I thought the job of the "beater" &/or his disciplined dog was to produce sport for the "shooters" who may or may not be interested in eating what they shot.
Yes you're right both, can to some people, be totally different scenarios but both do involve dogs working through cover & above ground.
Again to the individual who started this thread... good luck with your terrier!