We've gotten a bit spoiled in today's age, as most domestic machines all take the same size of needle. Until after WW2, and most manufacturing moving to Japan (and incidentally, going with the size Singer used for needles) most manufacturers had a specific size of needle for their machine. The interesting part is that Singer decided to go with the needle more commonly used in Eurpopean machines. And as Singer took market share, more companies started going with "Singer" size needles on later machines made in the US.
Nowdays, when most people say "size" they are referring to diameter or tip point. "Universal" typically refers to tip point, meaning it's good for most fabrics. It will fit most modern domestic machines too, but that is because they all take the same size to start with. My LA and industrial Juki both takes different sized needles than the domestic machines.
I have a large collection of vintage machines. I think I have 10-15 different needle sizes to accommodate them.