Many zoos have within them a smaller petting zoo where small, tame animals can be petted or fed by the visitors to the zoo.
There are some common phrases in English that use the word "pet."
All the kids in class say that Angelica is the teacher’s pet. (teacher’s pet = a student who receives favorable treatment when compared to other students.)
Cutting one’s fingernails in public is a common pet peeve. (pet peeve = a human behavior that is very irritating)
High speed train travel through the state has become the Governor’s pet project. (pet project = a project that is favored over other projects.)