Boxer-type underwear for men come in all shapes and sizes as you well know. Or perhaps you don’t know. Boxers, as they are called, resemble the trunks that boxers typically wear, hence the name.
There are some significant differences between what men wear and what fighting boxers wear. First, the style of trunks that fighting boxers wear are much longer, often touching the knee (and this style for fighting boxers has changed over the years). They are extremely loose and baggy. The undergarments men might wear only go down to the mid-thigh. Yes, the shorts are loose (yet not as loose as Boxers trunks). the Boxers are made so that nothing inside the shorts are tight. And that’s an intentional design.
One significant requirement that sportsmen boxers have (that regular men don’t have) is the need for their shorts to stay on their hips during a long and sweaty match. The boxing trunks cannot even accidentally slither over the waist even a little (you see Boxers try to pull them up if they do and it’s an interesting sight when they try to do it with their boxing gloves). The boxing shorts are reinforced at the waist with heavy elastic or a tie-string. Boxer-style underwear, conversely, rarely use a tie-string to keep them from sliding down. Instead those shorts rely on elastic, a comfort designed specifically for the boxer underwear.
The similarities between what amateur and professional boxers wear and what normal men wear is that they are made from many types of material: silk, cotton, or a combination of the two often are purchased.
On a quick sidenote, I have also seen boxer shorts made from a fishnet type of material. I suspect the Boxing world has pretty much rejected that impractical material because then it would show the protective gear that boxers wear during a match. Mesh/Fishnet material for boxer shorts are found in novelty stores.
Obviously the mesh/fishnet type of boxers are not designed for comfort or practical purposes; they’re aesthetically pleasing and geared toward the romantic side of the equation.
Boxer shorts, then, are similar to what fighting Boxers wear in physical material (especially the silk and cotton varieties), but differ in length and whether or not they have a drawstring to hold them up. Another major difference is cost: boxing shorts are more expensive than boxer underwear. Specialty boxers, on the other hand, can be more costly initially, but may very well be worth the added expense.