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Now, a lot of people confuse it for a euphonium which looks like this:
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The euphonium gets bigger from the mouth piece to the bell/part where the sound comes from giving it slightly smoother sound, while the baritone is more cylindrical making it sound like a mix between a euphonium and trombone.
They're both similar instruments but they're not the same.
They are both use to keep time/the tempo in music pieces.