A pet is what you would call a familiar. They are different than spirit animals, as they are your companions. The best way I have found to discover your spirit/totem animal, is 1. it will be an animal you have been drawn to your whole life. 2. They will frequently appear in your dreams. 3. While meditating ask them to come forward to you and show themselves to you. This works the same in dreams. Its amazing what asking nicely can achieve.
You can also have more than one spirit animal. They serve as guides and will share their knowledge with us if we are open to them.
A familiar on the other hand, our witchy companion if you may. Will protect and warn us if danger is coming whether magickal or of this earth. They will also lend us their energy during our magickal workings. But most of all they are our pets and give us unconditional love.