Never heard of BR50s (always figured the bulge made a BR50 improbable or something), but I knew there were R50s.
I'm definitely no expert...was waiting for somebody else to figure it out, but nobody else had any clue so I decided to give a possible option that I knew was real.
Decided to try to Google BR50s like everybody else, got the same result. But if you know GE makes them then that's a lead he can follow...
Basically though the larger sized flood lights provide a wider beam, while the narrow/wide neck is kinda like the focus. Like an adjustable flashlight, with the same size reflector you can have a spot in the center or a more even flood...but a larger reflector will spread the light out more given the same focus.
If the problem is the screw type base though he could get an adapter and use a higher power (than what he has now) E26 BR40 and probably be just fine. I just noticed he's got an 85w in there (Mogul base is usually for 300+ watt and those R50s are 500-750w) so a 120w BR40 could work for him, but he may need an adapter. Sure would be easier/cheaper to use R or BR40s.
Edit:
But he may even be looking for a PAR bulb and/or something without a screw type base.