I think it is important to explain what specializing means. To specialize means that you have board certification in the field of study—in this case, wildlife or zoological companion animals (ZCA). This typically means years of specialized training and an examination. It is easy to confuse specialization with having a special interest, which means you are interested in the species or group of species.
As far as opportunities for specialists in these fields, for wildlife this typically is in the form of state wildlife veterinarians, or working for university, non-profit, or governmental organizations. There are very few wildlife specialists in the world, actually! For ZCA specialists, the field is growing a lot. Owners are demanding higher levels of care and with that, more specialists are needed for this section of the field. For opportunities, ZCA specialists can be employed in referral private practices, universities, large urban centers, non-profits, and others.
Something important to know about the field is that it is competitive. It also requires a person with a lot of drive, initiative to teach themselves and learn everyday even when you are no longer a student, and the ability to think outside the box. Working with non-domestic species requires comparisons to what you have learned about domestics, so you need to also make sure you have a very strong base in your knowledge from vet school.