Interesting information contained in this thread.
Steelhead are rainbow trout period. Rainbow trout are a morph from the original Pacific salmon.
Thus the Oncorhynchus genera tag. Steelhead are anadromous in the Pacific since they go to saltwater then freshwater to spawn. The stocked great lake steelhead are considered potodramous since they are always in freshwater but retain there steelhead name since they migrate upriver to spawn. Landlocked rainbow trout in inland Ontario lakes are referred to simply as rainbow trout as there is no spawning migration. Whew!
So there is Pacific salmon(Oncorhynchus)(includes rainbows), Atlantic salmon(Salmo)(includes brown trout) and char(Salvelinus)(includes lakers, brookies) in North America.
According to taxonomists the original trout is the brown(Salmo Trutta). 'Trutta' being latin for trout. Browns have evolved from Atlantic salmon bringing some identification problems here at times.
Oddly this thread has been edumacational.