To me someone who breeds JUST for the money without care for quality or individual quality of life would be more like a "puppy mill" breeder - let's just call 'em "mill breeders"! Then there are the "hoarders" - who breed and collect, collect and breed... again without care for quality or quality of life.
Again to me, a "backyard breeder" is someone who just breeds whatever they happen to have around as pets - regardless of registration, quality, etc. They may be ignorant enough that their horses aren't as well cared for as they could be, but generally they do care ABOUT their pets.
Kinda like an ex neighbor of mine who said she was buying two golden retriever puppies from a friend and keeping the male whole "so we can make some money off him", since he and his full sister came with registration papers. I asked her when she ws going to start showing him or working him in trials - she'd never heard of such a thing. I told her about getting health checks and OFA certifications for hip, elbows, patellas, etc. Again, all this was news to her. Then I launched into inbreeding!
These were people who let their female mixed breed stand in the middle of the street and bark all night every time she was in heat. They were amazed that I told them she was pregnant BEFORE her 3rd litter of puppies! They had finally gotten her fixed after that, but then thinking if they got a "stud dog" and his sister that they'd make money. Argh. They did end up getting one male puppy from the litter, and had him fixed. So they were and would have been backyard breeders, IMHO - but were willing to be educated and aware that they didn't need to go into breeding.
Then there are "Responsible breeders" - those who work to educate themselves... breed to better the breed as well as their own horses, and do it all with care for the individual quality of life not ONLY for their animals but also for themselves... breeders who can keep every foal that they produce until the proper home comes along - no "must sell to buy hay" or worse... "must sell to make room for new foals"! (I'm not talking about people who hit bad times or bad health and need to sell - just the folks who have "dispersals" 2 or 3 times a year!)