So, horses and donkeys are different species. If you look more closely, though, this definition doesn't quite work in the way we would expect. For example, dogs can interbreed with wolves to form fertile wolf-dog hybrids. This tells us that dogs are technically not a different species from wolves. There are many other examples of this.
Evolution occurs as species change through time, sometimes splitting into two species.
But this does not happen with extinct species. This is by no means the only problem, though. Fossils are formed so rarely and under such unusual conditions that very few animals which die become preserved. Some areas, however, tend to preserve quite a lot. This means that our view of what lived in the past is swayed by the conditions that prevailed at the time.