The most common trombone is in Bb but you can get, tenor Trombones that have been/are pitched in Bb, C, & A. Alto Trombones that are available in F, Eb, and at one time: D. Bass Trombones that can be (basically) in Bb, C, F, Eb, D & G. Contrabass Trombones that are available in F, Eb, CC,BBb, & AA. Sopranos that are available in C, Bb, & at one time: G. Sopraninos that are in Eb. Even the Piccolo Trombones are available in both Bb & C. Soprano, Sopranino & Piccolo Trombones are written in transposed treble clef because they are usually played by Trumpet players.
The standard tenor trombone is a Bb instrument BUT bass clef music for this instrument is written in C (i.e. concert pitch). All treble clef music is transposed to the pitch of the instrument. Eg. French horn, trumpets, saxes, clarinets. Why isn't bass clef music transposed to the key of the instrument just like it is for instruments playing treble clef? Why are the low brass parts (trombone, euphonium, baritone, tuba) considered non-transposing? This is inconsistent with all instruments. In the brass band each instrument’s music is written in treble clef and transposed to the pitch of the horns.
The Treble Clef parts in Brass Bands is tradition. The theory was that anyone could play any part (assuming Valve Trombones), with only the slide to learn if using a slide Trombone. It's not uncommon even today, of brass band personnel to play Eb Horn one year, Baritone Horn the next year, & possibly Flugelhorn the following year. But the Tubas in a sense, like the recorders, & even to a lessor extant Trombones, CAN be transposing instruments outside of the Brass Band. No we don't transpose the music, but to those of us multi-instrumentalists, we do, in a sense, transpose fingerings/slide positions. Eb Tubas, F Tubas, CC Tubas, BBb Tubas ALL read in concert pitch in Orchestral, Yet they don't finger the same notes the same way. Same is true of recorders, Soprano, Tenor, & Great Bass are in C, The Sopranino, Alto, Bass, & Contrabass are in F, But ALL Recorder music is in C Treble. When I play F Alto Trombone or Eb Alto Trombone, all of the positions are different for each note. All the music is in concert pitch except brass bands, no matter which Clef is used.
There are some examples of transposed bass clef - Strauss tenor tuba parts in B flat bass clef, for instance - but these are relatively rare. Some of the traditions for transposition for higher brass instruments come out of the time that they were not fully chromatic, and different crooks were used to put them in the appropriate key. Trombones never had to do this since the slide made them chromatic. As far as brass bands go, the transposed treble clef for everything (except bass trombone and percussion) is a tradition that developed to allow players to be moved to another instrument with little fuss if the band needed them there. An extra cornet player might be asked to switch to euphonium, and be expected to be covering the part in a week or two - learning a new clef would slow down his progress on the new instrument. These are generalisations - I'm sure that there were other reasons that these traditions developed, but since they're there, it's a good idea for any serious trombone player to be familiar with bass, tenor and alto clefs, as well as treble in B flat and in C.
I hope that makes sense