Number of teeth don't matter except for the length of the chain- more teeth, you either slide the axle forward in the dropouts, or add a link (halflink if you have access to one).

What DOES matter is the chain width the FW is designed for- There is a bit of a one way compatibility as 1/8" > 3/32". You can run a 3/32" cog/fw/chainring with an 1/8" chain, but you can't run a 3/32" chain with a 1/8" cog/fw/chainring.

Branding means little more than implied quality in this context.

Other than the width of the chain, they're all compatible, other than a bizarre deviation off of the beaten path that shimano took for their track bicycle parts in the late 70's, every bicycle chain has been 1/2" (measured from pin to pin) for at least half a century now.