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Common in American English, a dog's owner will be called the dog's master. Master: one having authority over. "When I say come, he comes. When I say go, he goes." Not used with cats. They do not obey the owner as much as a dog would. Only called master if the dog obeys or is trained to obey it's master. A well trained dog will do tricks for his master. Otherwise, the owner is is just an owner.

Very simple, they are just called a pet owner! Pet owner, Cat owner, Dog owner, Bird owner... It's not very hard at all. I hope I helped! (: If I didn't, I'm sorry. :/

yes, we michus sometimes have owners, because cat-slavery has not been abolished yet! curse you HUMAN SLAVERS! you may only feed us and take away our shit! and we NEVER NEVER have masters!!!!!!!!!!!!!

I think it has a free answer and all above is ok.