A rescuer does not keep more animals than they can look after properly. A rescuer seeks veterinary care for sick or injured animals and rehomes as many as they can.
Hoarders simply collect animals and keep on collecting. They seldom rehome. Their animals are often housed in conditions similar to the worst puppy farms and many suffer from serious neglect as was seen in this program. In some countries animal hoarding is seen as a genuine psychological illness which it is.
One of the worst cases I was ever involved in was nearly 60 dogs and puppies and 30 plus cats INSIDE a house. The woman involved had once been a dedicated rescuer and was very highly thought of in welfare circles. However she grew too old to cope with huge numbers and her son added to the problem by breeding and showing dogs. Son had a nervous breakdown and ran away. Old woman had a stroke. She lay on her own surrounded by her animals for at least 3 days. When welfare workers (myself included), police and dog rangers entered the house we virtually ice skated on a sea of wall to wall sh*t.
The old lady was hospitalised and van after van loaded with animals made numerous trips from the house to the animal refuge. The dogs and cats ranged in age from a litter of new born puppies to a dog and cat in their early twenties.
It's very sad when a rescuer turns into a hoarder.