my aluminum rims on my trailer do carry a max load AND max PSI rating. as do the steel rims on my cargo trailer. And the rims for my truck.
On steel wheels the max PSI is often stamped on the inside of the rim. On my aluminum rims, I went to the mfg web site, found my rims, and it gave the Max PSI rating.
the steel rims were rated for "D" load range, the aluminum rims rated for 80psi cold.
In general, the load and PSI ratings are consistent, at least on mine, given the acceptable max tire size for the rim width. The max Load corresponded to the max recomended tire size LR typically available. However, I'm sure there are exceptions so if in doubt check it out.