What is the difference between non-ruminant animals and ruminant animals?

Non-ruminants are considered monogastrics because they have a simple stomach. They cannot regurgitate partly-digested matter and rechew it because it is not necessary; they do not have a large rumen nor are many such animals herbivorous (except hippos, rhinos, rabbits/hares and equines, for example). Almost all non-ruminant animals are omnivorous or carnivorous. Animals that are herbivorous and are non-ruminants have a functional cecum that is used to ferment the food that they have eaten once it passes through the stomach and small intestine. Such animals are called "hind-gut fermentors," and yet are still considered non-ruminants. Non-ruminants that are not hind-gut fermentors include all primates, canines, felines, bears, weasels, skunks, pigs, and a number of rodents.

Ruminants are animals which have a four-chambered stomach specially designed for digesting plant matter. No ruminant animals are carnivorous or omnivorous by nature because their stomachs are designed to digest coarse hard-to-break-down material being plants like grass, not protein, (which makes up meat) which is much easier to digest for the average animal, ruminant and non-ruminant alike. The names of the four chambers of a ruminant are called the Rumen, Reticulum, Omasum and Abomasum, each with a different "job," if you will, that is responsible for the complete digestion of coarse plant material. They regurgitate food--called "chewing the cud" The rumen acts tile a huge fermentation vat where additional essential amino acids and proteins are made by the bacteria in the rumen from the basic forages the animal has consumed. Ruminant animals are much more efficient in turning plant matter in to high-quality meat. Animals which are ruminants include all bovines, cervids (deer, moose, elk, etc,) goats, sheep, antelope, wildebeest and giraffes.

Camelids (camels, llamas and alpacas) do not fall into either categories because they do not have a four-chambered stomach, but are still fore-gut fermentors. They are not non-ruminants either because they are still capable of "chewing the cud" just like true ruminants are. These animals are called Pseudo-ruminants because they are, essentially "false ruminants" due to the fact that they lack the rumen, only having the reticulum, omasum and abomasum.
Ruminants have 4 stomachs - rumen, reticulum, omasum and abomasum. Non-ruminants just have 1. The main difference is that the 4 stomachs allow the organism to digest cellulose (grass).

correction- ruminants only have one stomach but they have 4 compartments....