Breeding Rejects
I believe you will find that the histories of many breeds started with culls that were given away, instead of killed, and then became the foundation of a new breed.
The old breeders wouldn't let them in because they were what was considered culls, so they often had to start their own breed, and, in tit for tat fashion, they then rejected dogs who fit the original standard.
It use to be common for breeders at dog shows to talk about breeding more differences into their breed so that it would not look like some other breed.
If you remember when the show club started showing Border Collies and Australian Shepherds? At that time, time both breeds had an assortment of different traits which would often be found in puppies in the same litter.
Some of the working sheepherding dogs (in both breeds) were medium sized, limber, pick eared, and others were larger, heavier, and drop eared. Both working breeds had some dogs who were shorthaired like a husky and medium haired like the show varieties today.
Breeders/breed clubs had to choose which traits were going to be in show dogs - if they didn't we would still have this variation in show dogs of these breeds - and we don't. The standards do NOT read: Ears: any; Size: smallish, medium, or large; Coat: short, medium or long, etc.
One of the breeders told me that the majority of their club had wanted to choose one of the varieties, but had chosen a different one for their standard, BECAUSE THE OTHER BREED ACCEPTED INTO THE CLUB BEFORE THEM, HAD CHOSE THAT TYPE FOR THEIR STANDARD.
Think of it like flags. If the country next to you chooses the flag that you were considering, you choose a different one. If the North and South split, they chose different flags that don't look alike.
But in dog, there is a reason for the original type, and breeding to get more and more difference results in a gap, where the previously desired type was.