Ok run down....
1. You do undergrad, get pre-reqs, apply for vet school.
During this time you try to gain experience with vets and animals and maybe research. These are not internships, sure, some people may say they did an "internship" at a zoo or something else. It isn't the same as what is done after vet school. Most people gain this experience by working for a vet, volunteering or shadowing vets in whatever capacity they can find. Some get this experience through research.
2. You got to vet school.
3. You pass NAVLE and graduate from vet school.
After you graduate from vet school you can work on any species just about anywhere as a general practitioner. Except zoos. You won't be hired. You can try, but don't. You won't be hired. You want to work in a zoo or on zoo animals you will need a residency. Period. You could work with pet exotics provided the clinic you end up at has the appropriate equipment and supplies or will get them for you.
If you decide you don't want to be a general practitioner or want more experience before jumping into the deep end of being a veterinarian, you will then do an internship. An internship is a year long that is basically a more intense version of the 4th year of vet school. You will rotate through the service again (IM, surgery, Emergency, ECC, ophtho, cardio, derm, etc, etc). During this time, or maybe you will already know, you can decide if you want to jump into general practice after or if you want to specialize.
If you elect to specialize you then apply for a residency. A residency is typically three years in length involving only the desired "thing" you want to do. Such as small animal internal medicine. Or ophthalmology. Or radiology. Or dermatology. Or oncology. Etc. etc. If you are lucky, you get into a residency immediately after that one year internship, if you are not, you could be on the path of another rotating internship or a specialty internship. This often happens for those that want to pursue surgery. You can end up doing anywhere from 1-whatever specialty internships, however long it takes until a residency elects you or you decide to move on.
ABVP as some have mentioned is basically a certificate program. It isn't a residency (technically) though it appears you can go through what is kind of a residency now for it (didn't used to be that way). It technically isn't even a specialty. It is literally saying "yup this general practitioner has practiced for at least x years, has submitted y papers and has passed this one exam". You can NOT call yourself a specialist with this at least not in the sense of "I am a small animal internal medicine specialist". You can only say you are certified by ABVP. It literally doesn't increase your salary. Clients have no ****ing clue what it is or what it means, kind of like AAHA accreditation. Everyone strives for AAHA (and they should) but clients have no ****ing clue what that actually means. So, ABVP is just something "extra" you can do while in general practice if you are so inclined and you have the time and resources to accomplish it. It has no benefits to you other than saying you did the thing and you might get some magazines and decreased cost on CE.