What do we call animals that only eat plants?

Herbivores, and eating plants is much harder than eating meat. Plant cell walls are made of cellulose, and almost no animal produces an enzyme that can break it down - so every large herbivore is really running a fermentation vat full of microbes that can, and living off what they release.

The engineering splits two ways. Cows, sheep and deer ferment before the stomach in a rumen and bring the material back up to chew again, which extracts a great deal but takes time. Horses, rabbits and elephants ferment after the stomach in an enlarged hindgut, which is faster and less thorough - so they eat more and pass more, and rabbits recover the shortfall by eating some of their own droppings, which is not a quirk but a second pass through the system.

The teeth follow the diet. Grass carries silica and wears enamel down like sandpaper, so grazers evolved high-crowned teeth that keep erupting through life, and the appearance of those teeth in the fossil record is one of the ways palaeontologists date the spread of grasslands. Herbivores also tend to have eyes on the sides of the head for a wide field of view, where predators have them at the front for depth - the oldest rule of thumb in zoology, and a reliable one.