Original Answer: Yes.
[Edit]
Yes and no. Small bore trombones and euphoniums will not have the same size mouthpieces. The euphonium is a large bore instrument (normally). If you are playing a large bore Trombone, then the shank of the mouthpiece will be the same size, but depending on the mouthpiece make, model, etc, may or may not be the same. If you have a Schilke 52D mouthpiece, and you put it in a Euphonium, then a Trombone, then yes the pieces are in fact the same size.
It's different for most styles; jazz bands use smaller cup sizes like a 12C to play higher pitches, but marching and concert bands tend to use larger ones such as a 6 1/2 AL to play louder with a fuller tone.
There are different sizes of mouthpieces that you can get, some may be more suited for higher notes and lower notes than others. I used a euphonium with a larger mouthpiece than my own euphonium's and found it harder to play. Hope that helps.
Everyone is different, and how it feels to you is important, so the best thing to do is to try different sizes and see what feels and plays the best for you.
Rim
Wide: Increases endurance.
Narrow: Improves flexibility.
Round: Improves comfort.
Sharp: Increases precision of attack.
Cup
Large: Increases volume, control.
Small: Relieves fatigue, weakness.
Deep: Darkens tone, especially in low register.
Shallow: Brightens tone, improves response, especially in high register.
Throat
Large: Increases blowing freedom, volume, tone; sharpens high register (largest sizes also sharpen low register).
Small: Increases resistance, endurance, brilliance; flattens high register.
Not exactly but pretty close.
No there are many different sizes
They are the same thing so yes.
If the pipes of a baritone were straightened out it would be 9 foot (2.74mtrs) end to end, which is the same as a trombone and a euphonium.
Trombone and euphonium/baritone.
Tuba, it is the longest so it creates the lowest tones. In order it would be tuba, baritone and trombone. Baritone and trombone are basically the same but baritone sounds a bit better at the lowest part of its range.
The best brand for a baritone is selmer. the best brand is def king or bach
A baritone horn looks somewhat like a miniaturized tuba. A bass trombone is still a trombone, but slightly larger. It also has an F trigger, which opens up more tubing near the bell of the trombone and changes the note. This allows players to reach the range from a low E flat to a low B, which is physically impossible on a tenor trombone. Some bass trombones also include another trigger, G flat, which can be opened separately or in combination with the F trigger.
If the pipes of a baritone were straightened out it would be 9 foot (2.74mtrs) end to end, which is the same as a trombone and a euphonium.
Trombone and euphonium/baritone.
8notes.com but use trombone its the same
Tuba, it is the longest so it creates the lowest tones. In order it would be tuba, baritone and trombone. Baritone and trombone are basically the same but baritone sounds a bit better at the lowest part of its range.
The best brand for a baritone is selmer. the best brand is def king or bach
I'm not sure of them all, but I played trumpet for a few years, then moved to the baritone. The concert baritone is very large, and much lower in pitch, but it has the same fingerings. The only exception is the additional 4th valve key, which can be used for alternate fingerings. It's not necessary if you're just starting out, though. The marching baritone is small enough to march with, but is a lot heavier than the trumpet! It only has 3 keys, and has the same fingerings as trumpet. There is also a marching trombone that looks extremely similar to a marching baritone. 3 keys, trumpet fingerings, but the bell is shaped like a trombone. Hope this helped!
they all contain reeds
The mouthpieces of a clarinet and a bass clarinet are identical in design. Where they differ is in size alone.
A baritone horn looks somewhat like a miniaturized tuba. A bass trombone is still a trombone, but slightly larger. It also has an F trigger, which opens up more tubing near the bell of the trombone and changes the note. This allows players to reach the range from a low E flat to a low B, which is physically impossible on a tenor trombone. Some bass trombones also include another trigger, G flat, which can be opened separately or in combination with the F trigger.
There are many instruments that look the same as a tuba, but are a different size so produce notes at a different pitch. These include euphonium, baritone and tenor horn. Trumpets and cornets are like a very small tuba turned on its side.
euphonium. same as the baritone.
Same as B-flat.