The "act" of a pet consuming or chewing on something, whether the action is appropriate or not (pica).
Refers to the act of a pet eating something, whether the action is appropriate (diet or treats) or inappropriate (feces, plants, wires, etc.). "Pica" is the proper terminology for consuming non-food items, and is covered by this tag.
The act of eating encompasses chewing / mastication, but does not refer to aggressive biting.
For concerns involving the process of providing food to a pet, use feeding, which may also be used in conjunction with eating.
For concerns involving what is appropriate to feed to a pet, use diet.