A semi-feral animal is an animal that lives predominantly in a feral

Feral

A feral organism is one that has changed from being domesticated to being wild or untamed. In the case of plants it is a movement from cultivated to uncultivated or controlled to volunteer. The introduction of feral animals or plants to their non-native regions, like any introduced species, may...

 state, but has some contact and experience with humans. This may be due to having been born into a domesticated state and then reverting to life in wild conditions, or it may be an animal that grows up in essentially wild conditions but has developed a comfort level with humans due to feeding, receiving medical care, or similar contacts.

Definitions of semi-feral in relation to cat

Cat

The cat , also known as the domestic cat or housecat to distinguish it from other felids and felines, is a small, usually furry, domesticated, carnivorous mammal that is valued by humans for its companionship and for its ability to hunt vermin and household pests...

s vary, but essentially describe an originally domesticated cat that has reverted to the wild

Wildness

Wildness is literally the quality of being wild or untamed, but further to this, it has been defined as a quality produced in nature , as that which emerges from a forest , and as a level of achievement in nature...

 and is no longer owned or kept by someone. Semi-feral cats may continue to live in proximity to humans and may be accustomed to their presence. Feral

Feral

A feral organism is one that has changed from being domesticated to being wild or untamed. In the case of plants it is a movement from cultivated to uncultivated or controlled to volunteer. The introduction of feral animals or plants to their non-native regions, like any introduced species, may...

 cats on the other hand are generally agreed to be the descendants of domesticated cats that have themselves never been domesticated

Domestication

Domestication or taming is the process whereby a population of animals or plants, through a process of selection, becomes accustomed to human provision and control. In the Convention on Biological Diversity a domesticated species is defined as a 'species in which the evolutionary process has been...

. A semi-feral cat that mates and gives birth to a litter will produce feral offspring.

In the context of horses and horse breed

Horse breed

Horse breed is a broad term with no clear consensus as to definition, but most commonly refers to selectively bred populations of domesticated horses, often with pedigrees recorded in a breed registry. However, the term is sometimes used in a very broad sense to define landrace animals, or...

s, semi-feral animals are those which are often untrained but usually owned by individuals. They are allowed to run in a natural state approaching that of wild conditions, but are periodically rounded up for assorted reasons, such as to wean foal

Foal

A foal is an equine, particularly a horse, that is one year old or younger. More specific terms are colt for a male foal and filly for a female foal, but these terms are used until the horse is age three or four. When the foal is nursing from its dam , it may also be called a suckling...

s, administer routine or emergency veterinary care, and so on. An example is the Camargue horse of France. Truly feral

Feral

A feral organism is one that has changed from being domesticated to being wild or untamed. In the case of plants it is a movement from cultivated to uncultivated or controlled to volunteer. The introduction of feral animals or plants to their non-native regions, like any introduced species, may...

 horses, such as the American Mustang

Mustang (horse)

A Mustang is a free-roaming horse of the North American west that first descended from horses brought to the Americas by the Spanish. Mustangs are often referred to as wild horses, but there is intense debate over terminology...

 or Australian Brumby

Brumby

A Brumby is a free-roaming feral horse in Australia. Although found in many areas around the country, the best-known brumbies are found in the Australian Alps region in south-eastern Australia. Today, most of them are found in the Northern Territory, with the second largest population in Queensland...

 have domesticated ancestors, but generally have no human ownership and live in essentially wild conditions, though they may also occasionally be rounded up for various management purposes. A true wild horse

Wild Horse

The wild horse is a species of the genus Equus, which includes as subspecies the domesticated horse as well as the undomesticated Tarpan and Przewalski's Horse. The Tarpan became extinct in the 19th century, and Przewalski's Horse was saved from the brink of extinction and reintroduced...

 can only be a horse without any domesticated ancestors. The only living, truly wild horse is the Przewalski's horse

Przewalski's Horse

Przewalski's Horse or Dzungarian Horse, is a rare and endangered subspecies of wild horse native to the steppes of central Asia, specifically China and Mongolia.At one time extinct in the wild, it has been reintroduced to its native habitat in Mongolia at the Khustain Nuruu...

.