From the way you worded this, seems you might never have heard a Ctb Bone + Tuba? You can't miss something you don't know!
Contrabass Trombone is reasonably similar to Cimbasso. They do have different bore and bell sizes and of course every horn company makes their instruments differently, but generally the audience isn't going to know the difference. Heck they won't even know the difference between Contra and plain old Bass.
Of course in a live recording setting all these instruments have different uses and pro orchestrators will know when to call on what. Cimbassi are more agile since they operate on valves than a slide, but typically your Bass Trombonists will not play the Cimbasso, it's a Tuba double. Contrabass Trombones can also play slide legato
and are more free-blowing (more efficient) in their very low range just above the pedal tones, while Cimbassi have to put all their valves down and this makes the horns very stuffy.
There are bigger differences between the subtypes of these horns - but there is no common distinguishing terms for their tunings. While in the world of Tubas we would have a CC pitched "Contrabass Tuba" and an Eb pitched "Bass Tuba" - in the Contrabass Trombone world, an F pitched horn is still a "
Contrabass Trombone" and
so is the one in BBb. However the two instruments have vastly different effective ranges and they do have different timbre too, since the lower horns often have larger bore size and larger bell throat, but again a typical movie-goer would be hard-pressed to know the difference between a Trumpet and a Trombone, let alone all these finer details.
However - just for you