Kris M. answered 07/07/19
Master of Science in Animal Science with 6+ years of Experiene
Herbivores tend to have a cecum, which allows them to digest cellulose, ligand, and other complex plant materials. Herbivores also tend to have "dull" teeth, like cows, to help grind down the plants as they are eating.
Carnivores do not have cecums, and generally have a smaller stomach and digestive tract; which, allows them to reduce time that food spends in their body so they can hunt more efficiently. Also, carnivores are often known for their "pointy" teeth and sharp claws that allow them to grip prey.
Regarding instincts, carnivores tend to have that stalking instinct in which they hunch down, stalk, and pounce on their prey (ex: large cats). Carnivores often evolve a great sense of smell or eyesight to hunt their prey (hawks- eyesight; snake- "smell"/ heat detection). Herbivores, on the other hand, have evolved a high "flight" response and are often found in large groups for herd protection.
Within omnivores, there is often cecum remnant. For example, humans have an appendix which is often thought to be a remnant of a cecum that digested plant matter. Additionally, omnivore teeth do not have strict "dullness" or strict "pointyness". Use the example of cow (herbivore) versus human (omnivore) versus feline (carnivore).
Let me know if you have any other questions!