To start off with (1st year of the basic vet degree) you learn the basic anatomy of one species(dog) and then later on you move on to do species differentiation once you know the basics (calf, sheep, horse, goat, pig), later on in the course (year 1+) you do a bit on exotics.
To practice on zoo and wild animals adeptly, most vets take advanced courses and degrees on exotic animal anatomy, diseases, treatment, husbandry, etc in wild/zoo/exotic/rare animals. Of course, many of the basic principles apply. A zebra is supprisingly like a horse inside, lion, like a very large tabby, etc.