Well the latin word vive means to live. So technically anything that an animal lives in could be called a vivarium.
Terr has something to do with earth and tends to house some sort of plants, as well as an animal

My advice would be that if you want an animal to live in a vivarium, get a lizard or snake. Very few tortoises are suited to living indoors in a vivarium.

The Tortoise trust website is very informative

Tortoise Trust Web - Indoor Housing & Vivarium Design