Bore
In this section
The instrument
Anatomy of the horn: the conical bore, the valves, the fourth valve, and the compensating system that keeps the low register in tune.
Is a euphonium a saxhorn
Historically yes — the euphonium descends from the B♭ saxhorn family patented by Adolphe Sax in the 1840s. Whether today's wide-bore euphonium still counts as a 'saxhorn' is a matter of how strictly you draw the family line.
Euphonium vs baritone — what's the difference
In British usage they are two different instruments: the euphonium has a wider conical bore and darker, fuller tone; the baritone horn is narrower and brighter. In American usage 'baritone' is often just a loose name for a euphonium.