A wild animal is an animal that is NOT domesticated by man, and lives in the wild. Even though some have been made into pets occasionally it does not mean they are any less wild.
Wildlife refers to all wild "living things". Not only "all" types of wild animals, but plants too. The animals include ones like Mammals, Birds, Amphibians, Reptiles, Fish, Insects and other Arthropods, Mollusks, Worms, single-celled creatures, and bacteria and viruses. The plants include ones like Trees, Flowers, Shrubs, Cactus, Grasses, Fungus like Mushrooms, Lichen, and Molds.
"True" wild horses are wild animals AND wildlife. Most breeds have been domesticated over thousands of years, but there are a few species of wild horses living in Africa and Asia. Ones in the USA are usually those that have gone ferile from many years ago, and can therefore be determined as wild.