What is the difference between literary Naturalism and Realism? Quote from two authors in your answer and try to identify key themes for Naturalism and Realism for each author you address.

It is easy to mix up realism and naturalism. Both share unsentimental, harsh views of life. Both focus often on social inequalities, poverty, and hardship. However, there is a strong element of social determinism (the idea that our behavior is determined by social and physical forces beyond our control) present in naturalism that is not in realism. Naturalism tends to operate in a godless, meaningless universe, while a realist novel could still value religious and spiritual perspectives.
Frank Norris's 1899 novel, McTeague, is a textbook example of literary naturalism. The main character, McTeague, is a poor Irish-American who gains some stature when he becomes a dentist. His wife, Trina, is from a family of relatively middle class German immigrants. Norris presents these characters as lacking in free will: when hit by poverty, McTeague and Trina revert to almost animalistic states, eventually abandoning their middle class values and turning on one another.
McTeague is also shown to be a sexual sadist and a brute due to his maleness. When he first meets Trina, who comes to him for a filling, McTeague is tempted to rape her while she is unconscious, so struck is he by her beauty:

McTeague straightened up, putting the sponge upon the rack behind him, his eyes fixed upon Trina's face. For some time, he stood watching her as she lay there, unconscious and helpless, and very pretty. He was alone with her, and she was absolutely without defense.
Suddenly the animal in the man stirred and woke; the evil instincts that in him were so close to the surface leaped to life, shouting and clamoring.

Norris goes on to describe McTeague's civilized persona doing battle with this "evil" and primitive instinct, and this conflict goes on throughout the book. However, McTeague succumbs to it in the end, a tragic conclusion foreshadowed here when McTeague forces a kiss on the unconscious Trina. Even if he does not rape her, he still can never fully resist the deterministic instincts which control him.
Literary realism is less dour. Depicting everyday life and common people are the main goals here. Mark Twain's The Adventures of Huckleberry Finn is a classic realist novel. It features a lower class boy as its hero, but Huck is not trapped by his environment the way McTeague and Trina are. Though raised in a society where black people are viewed as subhuman and slavery as moral, Huck changes his mind, even though he believes he will be damned to hell for helping runaway slave Jim evade the authorities.
Determinism definitely doesn't play as strong a role because Huck is fiercely independent. Even under the influence of the moralistic Widow Douglas, he refuses to be tamed:

The Widow Douglas she took me for her son, and allowed she would sivilize me; but it was rough living in the house all the time, considering how dismal regular and decent the widow was in all her ways; and so when I couldn't stand it no longer I lit out. I got into my old rags and my sugar-hogshead again, and was free and satisfied. But Tom Sawyer he hunted me up and said he was going to start a band of robbers, and I might join if I would go back to the widow and be respectable. So I went back.

So, these are the most significant differences. Both of the aforementioned novels aim to show the everyday and mundane in their settings and characters, but naturalism is by far the more pessimistic of the two when it comes to ideas about human nature.