For bikes I've always used Phil because it was readily available in shops back in the 1970s and it works. But it's probably just marine grease and if I needed to use grease more often it'd be cheaper to buy a tub of marine grease and an applicator.
If you check RJ the Bike Guy's YouTube channel he's about as practical as they come, to the extent that he'll use an adjustable wrench sometimes rather than fish around in the toolbox for a specific size wrench. But RJ does use both marine and lithium greases, although I haven't noticed any particular pattern in specific applications for each.
Spring piston airgun aficionados may use several types of greases -- to reduce harsh spring vibration, or to prevent migration of combustible grease/oil into compression chambers, etc. -- but bikes don't seem to be that picky. We don't go fast enough for hub grease to matter, and as someone else noted headset grease is mostly to protect against corrosion -- the bearings hardly move at all compared with hubs and bottom brackets.
Regarding friction, I doubt any of us generate enough power for it to matter how much grease we pack in. And any excess gets forced out anyway. Back in the '70s it was trendy to substitute oil for grease for competition, at least with hubs and bearing surfaces designed for it. Made zero difference in my use and demanded a lot more maintenance. There's also some slight ticking noise from the ball bearings in oil.
Grease lasts longer, occludes entry from water and debris. I fill the cups with grease and wipe off the excess after reassembly, and again after a couple of rides.
The only bike components where I've noticed any differences in lubes and techniques are chains and rear derailleur pulleys. Even those differences are minor, but enough that it would matter to the strongest riders.