The baritone and euphonium horns are distinguishable due to differences in their shape, which causes variations in sound. Other factors used to tell the difference include the direction of the bell and the number of valves. These are not as definitive.
Perhaps the most notable difference between the baritone and euphonium is the size of the bore, or inside chamber of the instrument through which air passes when the player performs. The baritone has a slightly smaller bore than the euphonium does. Additionally, the shape of the tubing in a baritone is mostly cylindrical, whereas euphonium tubing is conical.
On most instruments played via an air stream, the shape of the bore determines to some degree what the size and shape of the bell will be. Subsequently, baritone horns, with their smaller tubing, have slightly smaller bells than euphoniums. Overall, the smaller tubing and bell make the baritone a less bulky instrument to hold and play.
The differences between the tubing and bells of the baritone and euphonium horns causes differences in the tonal color produced. These differences are recognizable to the trained ear. Baritones tend to have a brighter, lighter sound than euphoniums, which is good for cutting through an ensemble. Euphoniums, by contrast, have a mellower, warmer sound, which players and composers prefer for solos or when the ensemble needs to sound solid and deep. This is a generalization, however, as some baritones are constructed in such a way as to produce a color very similar to the technically larger euphonium and vise versa.
People sometimes refer to the number of valves on a baritone and euphonium to make a distinction between the two instruments. A euphonium is more likely to have four valves, while a baritone usually has three. This is another characteristic that cannot be used with definitiveness, however, because some baritones in fact are constructed with four valves.
When marching bands needed a valved tenor brass instrument in the 20th century, band directors and instrument makers designed an instrument that, because of its bore size, was technically a hybrid of the baritone and euphonium. This instrument had a bell that pointed forward, which let the sound carry readily toward the audience in the direction the performer faced while marching. The tendency, despite the hybrid nature of the instrument, was to call it a baritone. This stuck, so modern players and directors sometimes refer to any baritone or euphonium or hybrid of the two with a forward-facing bell as a baritone.
An additional reason people have confusion between the baritone and euphonium is that manufacturers of the instrument had a poor practice of labeling student model instruments as baritones and upper level or professional models as euphoniums. They did this even when the student model was by all accounts a true euphonium. This tendency caused some people erroneously to believe that the only difference between a baritone and euphonium was grade or quality.
Even though the baritone and euphonium have some clear distinguishing characteristics, the instruments are highly compatible with one another. Both instruments are able to fill the need for a tenor brass voice in an ensemble. They play in the same range and overtone series and thus use the same fingerings, so baritone players usually can play the euphonium and vise versa with slight adjustments. The pitch and fingering similarities mean that baritone players may perform pieces written for euphonium and that euphonium players may perform pieces composed for baritones. Many ensembles use a mixture of the instruments, but others are pickier and use only one or the other, depending on the sound the director wants.