If total difficulty is X and the ratio for full blocks to candidate blocks shared with the pool is Y, then the candidate block PoW now has to meet X/Y while hashing the candidate block PoW + the pool's commitment hash must meet Y, which together makes for X/Y*Y and thus the same total difficulty.
The main differences are that there's a public key identifier the miners are told about in advance and expect to see in block templates, and that that now the pool has to publish this commitment value together with the block that also contains the commitment hash, and that this is verified together with the PoW.