Each breed has a "standard". The standard is the written list of physical and temperament characteristics that a breed is supposed to embody. Basically a definition of what each breed is. Look up any breed's standard and you will see specifications on color, size, body proportions, temperament, coat length and texture, etc.
Each registering body (AKC, UKC, CKC, etc.) may have slightly different standards for any given breed. For example, some registering bodies will accept certain colors whereas other registering bodies will consider those colors to be faults. For some breeds it might be head size, muzzle shape, or something else that differs between the standards of the different registering bodies.
It is not unusual to see different "types" of the same breed in different geographical regions of the world--sometimes even within the same geographical region--depending on which is the more prevalent registering body for that region and how their standard reads.
Boxers bred from European lines tend to be wider through the shoulder, have a shorter, more upturned muzzle, and a different head shape than those bred from American lines. They are all Boxers, just bred to slightly different written standards.