There has been so much confusion for soooooo long about the difference between baritone and euphonium that I wrote a monograph a few decades ago, which later become this web page:

http://www.dwerden.com/eu-articles-bareuph.cfm

I think it helped many to understand the technical differences. But there is nothing like seeing and hearing the different horns in action, so I recently recorded on video the same song, played in the same room, recorded on the same equipment, played on euphonium, double-bell euphonium, and baritone horn.

The double-bell is an interesting instrument (now extinct). The large bell definitely has a euphonium-like sound, although it is not as big as today's euphoniums. The small bell is actually a slightly smaller sound than on my baritone, although my baritone had a bigger sound than some earlier models. If you ignore the small bell, you have a horn that was used in most public schools the most of the 20th century (until upright, front-valve euphoniums started to take over). Those horns were often called "baritones" out loud and at the top of the sheet music. However, the fit all the technical/design definitions of a euphonium and have the round sound of a euphonium.

The horns used below are:
Euphonium: Adams Custom, with .60 brass thickness and a sterling silver bell, 4 valves compensating. Bore: .592"
Double-Bell Euphonium: Holton from about 1935; 5 valves (4 for playing notes and 1 for switching bells). Bore: .560"
Baritone Horn: Besson Sovereign 955 (from around 1982), 3 valves, compensating. Bore: .515"

Euphonium:
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Double-Bell Euphonium:
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Baritone Horn:
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