Most of the descriptions have been nicked from Wikipedia, as brass in general is not my level of expertise! So this is a general list, which will be amended as other members of the band pile abuse and corrections on my unprotected and balding head.
Basically, they all go “parp” when you blow down the narrow end!
There’s an explanation as to what we mean by “plays in Bb” below…
The Cornet, playing in Bb, is the “soprano” of the band - it generally plays the tune and the upper harmonies. Occasionally known by the disrespectful as a “squeaky trumpet”!
The Tenor Horn is pitched in Eb and, as its alternative name “Alto Horn” suggests, fills out the top harmony line.
The Baritone Horn plays in Bb, an octave below the Cornets. Part of the “tenor” section of the band, its tone is halfway between the brightness of the trombone and the mellow sound of the Euphonium.
Euphonium is Greek for “sweet-voiced” - playing in Bb, it plays in the same tenor range as the Baritone horn but has a mellower sound.
The Trombone is a development of the sackbut from the middle ages. With no valves, it is is played by using the slide to obtain the various notes. It is pitched in Bb, the Bass version having a larger bore and deeper sound.
The Big Daddy of the band. The Bass, or Tuba as it is sometimes called, can be in Eb or, playing even lower, Bb and provides the groundrock bass line for the band.
What do we mean by “plays in Bb or Eb”?
Essentially, it’s the basic note that you get when you blow down the thing with no buttons pushed (or valves, as we say) or, in the case of the trombone, with the slide closed. Brass Band instruments are generally treated as transposing instruments, which means that as far as the written music is concerned, you ignore the actual note you are producing and work on the assumption that when you play this basic note, you are playing the note C (even though you are in fact, playing a Bb or an Eb).
The reasons for this are lost in the mists of time, but the most important thing is that it makes the music easier to read as you tend to have less sharps and flats to worry about. The other thing that is different about brass bands is that the music is written in the treble clef, no matter what the range of notes that you are actually playing. Again, this is a historical matter and makes no real sense at all…
All the above is true for all the instruments except for the Bass Trombone, which has its music written in the bass clef and plays in Concert pitch (which means the music genuinely reflects the notes played). All this does is adds to the general confusion, worries the conductor, and muddles the poor bass trombonist no end when someone hands him the music for for the 2nd trombone in the treble clef and expects him to sight-read it!