Yup, they're the same species. The steelhead is a rainbow that goes to sea-- or in the case of the steelhead introduced into the East, the Great Lakes.
There are several different "strains" or races of steelhead in the wild, with different growth rates, differing years at sea, and the timing of their runs up into streams, and these have been propagated in hatcheries and introduced through stocking programs. Here in NY most of the steelhead return in to the rivers in the fall, then spawn in early spring, but some strains like the Skamania are "summer run" fish that return in late spring and hold over into the early spring of the next year to spawn. Telling different strains of steelhead apart can be very difficult, and the longer they remain in streams the more they start to resemble rainbows.
But in general, steelhead have a much more silvery appearance, a greenish-blue back and less spotting, with few, if any, spots visible below the lateral line. Because of the greater food available, they also tend to be larger than "resident" (nonmigratory) rainbows of the same age. Rainbows by comparison typically have red on their cheeks, and the characteristic prominent red stripe along their sides. As steelhead spend more time in the stream they tend to get darker and take on more of the rainbow's coloration. You can't always rely on size alone, especially in the PNW, but in many areas where they have been introduced, they are "impossibly large" in terms of what a stream could be reasonably expected to support in comparison to the resident trout that don't have access to the rich food sources of baitfish in lakes/ocean.
Another way to tell, in most hatchery supported steelhead fisheries, steelhead are fin clipped to distinguish different stocks of fish and there is usually info on the state's DNR website that will tell you the "code".
There are also "sea run" forms of other trout and char, including sea run cutthroats in the Pacific Northwest, sea run brown trout (found mostly in Europe), sea run brook called "salters" and "coasters" in New England, and if I'm not mistaken the sea going arctic char is now thought to be the same species as dolly varden which lives it's life in streams. These "sea run" forms go through an additional phase in their development as do steelhead and pacific and atlantic salmon where they turn from parr into "smolts" before going to sea. "Resident" trout and char don't go through the smolt phase.
Here’s pics of some beautiful rainbows in Troutdawgs recent post. Note all the spots below the lateral line:
Compared to these fish caught by George McFly and his buddy. Some of these fish have been in the stream awhile and have darkened up a bit, and the stripe is starting to appear, but note the lack of spotting below the lateral line. The fish in the bottom 3 pics look like they’ve been recent arrivals from the lake:
And here’s some steelhead caught by Doublelung. Note that some have “darkened up” some from being in the river awhile, but the fish in the pic second from the bottom looks like a fresh “chromer” just in from the sea (lake in this case)