There are thousands of brands out there. Most are only sold locally, or regionally, though.
Many of the common brands manufacture their own ammo. But, they also make ammunition and components for each other.
For example...
Sellier & Bellot currently makes the Winchester "Metric" line of ammo, but Prvi Partisan made it in the past (and it was better ammo).
ArmsCor made the majority of Fiocchi rimfire ammo imported into the U.S. for several decades.
CCI currently makes Fiocchi .22 WMR and a couple specialty .22 LR loads, as well as almost all brands of .17 HMR ammo, and most .17 HM2 ammo.
Aguila uses Eley rimfire hulls.
And the list goes on...
And, some of the different brands are essentially one entity.
ATK owns Federal, Speer, Blazer, CCI, and a bunch of other firearms and ammunition related companies and their subsidiaries. Most Blazer, CCI, Speer, and Federal handgun brass comes off the same production lines.