I have a really large B flat tuba and smaller B flat tuba - far more difference in their sizes than the difference between a B flat bass trombone and a B flat tenor trombone - both of which are responsible for just about completely the same range, as one plays lower better and one place higher better (just like my two B flat tubas)... and yes, I use different mouthpieces with my two B flat tubas, but the fact that I have both of them doesn't mean that one of them is a "double"... and I don't "specialize" in one or the other of them.
Many trumpet players have or even carry a B-flat, a C, an E flat, and a piccolo... and they think of them as their "trumpetS", rather than any of them being "doubles"... and not even their flugelhorn or their cornet... even though (unlike the bass trombone and the tenor trombone) some of them are built to different lengths.
Trombone, tuba, or tenor sax would be considered "doubleS" for a trumpet player.
