Even on something as simple as a trumpet, around the turn of the 20th century, manufacturers were characterizing their bore sizes as "0","0-","0+","1","2" with no consistency between manufacturers. Then you have multiple types of instruments, so the same ACTUAL bore size may be a large cornet, medium trumpet, and small trombone.
Bring on the tuba. First you had very small horns, that were used in the town band for both concerts AND marching by tubists who could only afford one horn. Bigger horns, which sounded better, were available, but only usable by stout fellows. Then you got concert-only horns, which became the norm. Since "bigger IS better", soon people were making "Monster Bore" tubas.
Add to that the difference in the bugle were rotary valves and piston valves occur. Valve bore size then becomes incomparable between valve types. So SOME type of comparison and description of playing quality and physical size is needed. Enter the -/4 descriptions.
The pre-sousa concert/marching horns were characterized as 1/2. A "full size" concert horn is 4/4. A "midway in between" horn is 3/4. A "Monster Bore" became 5/4. What was considered a absolute whale, since people have grown in the last two centuries, along with their playing abilities, is "6/4".
Who gets to make the characterization? The manufacturer. Is there any rhyme or reason? No, but if it's too far out of subjective whack, the world will likely call them on it and give it their own characterization.
The characterization of key makes about as much sense. Start with the French tuba in "C" above the "Bb" trombone. Following this lead, a tenor tuba (or a baritone or a euphonium) would be in Bb. Contrabass tubas, to distinguish the octave difference, became CC/BBb. Bass tubas were in F or Eb, but again, some manufacturers, wanting to stress size, go with EEb. F tubas are usually just called "F" (without regard to octave).
Again, Who gets to make the characterization? The manufacturer. Is there any rhyme or reason? No, but if it's too far out of subjective whack, the world will likely call them on it and give it their own characterization.
So, like many things in the world of music, the answer is, "it depends".



