I know that the Baritone is different from the Euphonium because it has a narrower bore and sharper taper, esp. in British bands, but my question is are there precise measurements that define whether a horn is a baritone or a euphonium, or is it at the manufacturer's discretion?
I have strong reason to believe alephzero is correct and LaurencePayne is wrong. Wikipedia backs up what I remember from my wind ensemble days:
The euphonium and the baritone differ in that the bore size of the baritone horn is typically smaller than that of the euphonium, and the baritone is primarily cylindrical bore, whereas the euphonium is predominantly conical bore. The two instruments are easily interchangeable to the player, with some modification of breath and embouchure, since the two have identical range and essentially identical fingering. The cylindrical baritone offers a brighter sound and the conical euphonium offers a mellower sound.
The fact that they look similar externally does not make them the same, any more than a trumpet and a cornet are. The shape of an instrument's bore is critical -- look at the sound difference between a clarinet and a saxophone. It's not the material. I've played metal clarinets; they sound like any other clarinet. Bird played a plastic alto on occasion; it sounded sorta like a brass sax.
Both Laurence user 19146 are incorrect.
the difference is that the baritone has a cylindrical bore, and the euphonium is conical. the conical bore forces the euphonium into a slightly bigger frame, but this difference is too small to be used to differentiate, especially when comparing a large-bore baritone to a small-bore euphonium.
both baritones and euphoniums are available in 3-, 4- and 5 valve variants, both can be compensated or not, and both are seen with and without triggers.
To my knowledge, the "average" bore size of the euphonium and baritone are roughly the same, which is also why they are nearly fully interchangeable (and the source of the confusion).
Left: Besson Class A - in the niddle: Courtois - right: Yamaha
The Euphonium and Baritone are all the same pitch but the sound and the size of the Baritone is thinner.
That means the Bariton has obvious the same length, but some Euphonium have a compensating system and the sound is more voluminous. That’s why it can be called also small tuba. The mouthpiece is bigger too.
Not all Euphonium have 4 valves and not all have this compensating system.
It plays the counterpoint to the cornets and because of this function it is also called the cello in the brass band, while the sound of a Baritone is rather like a Trombone (the the pitch of a Flugelhorn is an Octava higher!)
The biggest difference between them is the price.
There is no official specification. Your general description is correct. We agree that the euph. is more conical, the baritone more cylindrical. But the baritone is far from perfectly cylindrical - look at a picture of one - and there is no official specification as to HOW non-cylindrical it may be. There are 4-valve baritones, there are 3-valve euphoniums.