General Terms:
* Fauna: This is the most general term and refers to all the animal life in a particular region. It's often used in scientific contexts.
* Wildlife: This term usually refers to animals that are living in their natural habitat, often in a wild state.
* Zoogeographic region: This term is used to describe major geographical areas with distinct animal communities, like the Nearctic, Palearctic, etc.
Specific Terms:
* Avifauna: Birds of a region.
* Ichthyofauna: Fish of a region.
* Entomofauna: Insects of a region.
* Herpetofauna: Amphibians and reptiles of a region.
Additional Considerations:
* Ecosystem: You could also refer to the animal kingdom of a specific ecosystem, like the "fauna of the rainforest" or the "wildlife of the savanna."
* Biogeographic realm: This term is used to describe very large areas with distinctive animal and plant life, like the Neotropical realm.
Ultimately, the best term to use will depend on the specific context and the level of detail you want to convey.