Franchise mode is online, so all animals you buy there are from other people unless it's from Frontier Zoo (there's at most 4 or so frontier animals so the market is never completely empty). If you don't want to play online, then play challenge mode. It's exactly the same as franchise, but offline, so you're not getting animals from others.
Transferring animals between zoos is only possible in franchise mode, and people do it for a number of reasons. The most common reason is to transfer over a couple animals when starting a new franchise zoo, so you don't have to spend thousands of CC buying whole new animals. So if, for example, you have gold-medal tigers in one zoo, you can transfer some of them to another franchise zoo so you don't have to spend currency or start out with poor stat, no medal animals.