When Show Boat premiered in 1927, many people thought that "Ol' Man River" was little more than a Black spiritual adapted for the musical.
It was kind of like how some people (cough, Ronald Reagan, cough) thought that "Edelweiss" from The Sound of Music was the Austrian national anthem. Both instances score major authenticity points for Oscar Hammerstein (and one scores a major "oops" for President Reagan).
As it turns out, "Ol' Man River" is a rewrite of the play's opening number, "Cotton Blossom" (the "Cotton Blossom" chorus is refrained partway through the song). The notes are slowed down and sung in an inverse order, but on the whole, the two songs are largely the same and can be solidly categorized as musical theater numbers, not traditional spirituals.