All are large rifle primer except Remington. I have a Ruger M77 7.62x39 in which the firing pin hit is a tad off from center...with it, I have experienced a failure to fire or 2 when using Remington brass for reloading. Since I deer hunt with mine, that is no good, so I use large primer cases. In my Ruger Number 1 in 7.62x39, both small and large primer cases fire fine. I also have about 20,000 reclaimed USGI 30 carbine primers ($6 per 1000), so I use the Remington cases with them for practice/plinking.
So, other than my rifle pickiness and the fact that I have lots of small rifle primers to use, for most people I see no practical difference between small and large primer cases. I have no idea of who makes the ammo for those companies, but suspect they all make their own. I do note that the brands of brass weight differently, but have seen no impact point differences with my reloads up to 150yd (the length of the range) when using the same bullets.