The 3 1/4" CAN be a full nitro, only with the same power working at lower pressure-much like the .500 3 1/4" is to the .500 3", but these are, I think, rare, and the 3 1/4" version as mentioned above was mostly seen in BP guise at an earlier basis.
The 3" can be either BP or full nitro.
Same for the 2 3/4", although the 2 3/4" full nitro is less powerful than either the 3" or 3 1/4".
And, then we have the un-ending list it seems, of "tropical loads", supplied by different makers in the hey-day of these cartridges, which makes things even more confusing.
However, the most well known, legendary, and common of the whole lot, was the 3" full nitro.
Also, what I will not go into at this point, because it would become confusing, is the different bullet weights in all three case lengths. The 650 to 750 in all three, and so-on, so-on.
But, rest assured, when the .577 is mentioned anywhere in a crowded bar-room, that it is the 3" case nitro with the 750grn. bullet and 100grs. of cordite that is being spoken of.