Sorry to have to disagree, but a Bb trombone is NOT the same as the 'orchestral' C trombone. Both are often referred to as a 'tenor trombone', which perhaps confuses the issue a little for the uninitiated - but no more so than having clarinets in different pitches (C, Bb, A etc.)...

'Bb/C' trombones are available, usually with a rotary valve to permit the player to switch pitch - see this old Conn/Wurlitzer model dating back to 1914!