Pets4Homes is not a puppy farm, it's a website where people can list animals they have for sale. Anyone can post on there, so, a lot of puppy farms list their animals on there.
To me the definition of a puppy farm is someone who is breeding puppies with a main motivation of profit without regard for the welfare of the animals. e.g., trying to maximise profit by getting the bitch pregnant as soon as possible, keeping breeding bitches until they are exhausted and then discarding them, the animals may also be kept in unsanitary and cruel conditions, they might not have space to run around and play or proper care etc. They don't care if the litter has several dead or unhealthy puppies as long as there are enough to turn a profit. They don't care if the puppies go to happy homes with good owners or any old person with whatever motivation as long as they get their money.
If you want a pet, then presumably you love animals and want to give them a happy long life free of unnecessary suffering. If you buy from a puppy farm, your cute puppy has come at the expense of the life of another dog or multiple dogs, who will only ever know suffering because they are being used for multiple pregnancies (or puppies born unhealthy who are left without care because they aren't profitable). Morally, that doesn't seem right for an animal lover to support something like this. Of course most puppy farmers try to hide the fact they are farming and pretend the litter was accidental or they did it "for the kids" etc.
Even if you have purely selfish motivations and don't care about the suffering of the mother dog, puppies from puppy farms can be born with health issues because they haven't been bred responsibly (especially fashionable breeds) or they can come to you riddled with fleas, worms and lice with poor socialisation because they have been removed from the mother too early and not had any experience of a normal family home.
Backyard breeders are probably somewhere in the middle, not necessarily cruel in intent, but may overlook several things which are important for the health of your dog. But as said, most puppy farmers will make out that they are amateur/backyard breeders.