What you say explains why some animals are faster, able to eat differnt foods but does not explain how one animal can change into another unknown type of animal.
One animal doesn't change into another unknown type of animal.
In a population of a particular species, individuals will vary, with some having traits that give them an advantage over the average individual, and some having traits that put them at a disadvantage - in terms of having viable offspring. When the traits are heritable (passed on to the offspring), the offspring will also have those advantages or disadvantages.
Consequently, over the generations, an increasing proportion of the population will have the advantageous traits (because they tend to have more offspring than average), and a decreasing proportion of the population will tend to have the disadvantageous traits (because they tend to have fewer offspring than average). This is the population evolving.
If conditions are severe or change rapidly (a new predator, competition for food, a climate or geographic change, etc), small advantages can make a big difference to survival and reproductive success in each generation, so may rapidly accumulate, resulting in large changes from the original population.
For example, slow-moving herbivores on a species may be taken by a predator that can't catch the faster ones, so only the faster ones survive to reproduce, changing the herbivore population balance in favour of speed. Faster predators then have an advantage over their slower fellows, and the predator population will also change in favour of speed, resulting in an evolutionary ratcheting effect between predator and prey populations for speed - an evolutionary 'arms race' (literally, a legs race).
Alternatively, there may be herbivore variants that are bigger and more aggressive than their fellows, and can defend themselves and their young against the predators. The balance of the population will then tend towards those that can effectively defend against the predators. The more intelligent predators will then have an advantage among their fellows, in devising ways to separate the more vulnerable prey from the defenders, and so-on.
The speed selection and the defence selection could occur in separate populations of the same species, so that, over evolutionary timescales, the accumulations of small but advantageous changes might make such large changes in the morphology and lifestyles of those populations, that they look like different animals altogether (slim & fast vs big and aggressive).