The difference? One has two words and the other has three words.
The difference between a steelhead smolt and a rainbow trout is that the steelhead smolt has undergone smotification and possesses the ability to enter the ocean.
Genetically, they differ only slightly. That's why the same genus and species name applies to both.
Hatchery juveniles that haven't undergone smoltification are released into the river when they are at the right size. That "right" size is determined by approximately how big they will undergo smoltification (turning into a smolt). If the fish are kept in the hatchery and continue to grow, the fish will not undergo smoltification and will become a resident rainbow trout instead.
Most juveniles that are released into the system will migrate downstream and become smolts. A small percentage of the fish will remain in the system, possibly due to the abundance of food source, and residualize instead. These fish will eventually become resident rainbow trout, which are potential predators of other juvenile salmonids. They are also competitors of wild steelhead smolt.
In order to reduce negative impacts of hatchery steelhead that have residualized, anglers are allowed to catch and keep four of these per day. What people should not be doing is to keep the fish without identifying them first (hatchery or wild).