First, there is no relation between the two Richards, who ruled England nearly 80 years apart. Just the briefest of history lessons: Richard II was deposed by Henry IV, whose grandson Henry VI was deposed by Edward IV, who died leaving the throne empty for his brother Richard III.
As I mentioned, I have study Richard III quite a bit, two years ago I wrote a 6 page paper in defense of Richard, and last year I wrote a 16 page paper defending him and comparing him to a character in a German novel who I saw as very similar. Let me set up my defense of Richard, but with one caveat: I do not condone Richard for what he did. He is a villain, a devil, an evil, evil man who committed many atrocities. But, I can begin to understand him and where he came from.
The question is asked again and again, "Why is Richard the way he is?" And for me, part of the answer has to be, That is the way society made him.
1. His Deformity -- Richard is ugly, and in the Elizabethan era there was a strong belief that the outer appearance reflected the inner, that the way a person looked could tell you about the state of their soul. (see Elizabethans at Home, by Lu Emily Pearson, page 80). Shakespeare references this belief in Henry VI, part 3, with Queen Margaret's line where she refers to Richard as "a foul misshapen stigmatic, / Mark’d by the destinies to be avoided” (2.2.136-37). His entire life he has known that he is deformed, and has heard that his deformity is evidence of some evil innate in him. Almost every monologue Richard has makes some reference to his appearance and the inequalities that nature has placed upon him.
Why, love forswore me in my mother's womb: / She did corrupt frail nature with some bribe, / To shrink mine arm up like a wither'd shrub; / To make an envious mountain on my back, / Where sits deformity to mock my body; / To shape my legs of an unequal size; / To disproportion me in every part, / And am I then a man to be beloved? (Henry VI, part 3 3.2.153-163)
2. His life as a Soldier -- Richard is the younger son of a noble family, which means what? He gets very little. Younger sons usually joined the Church or the military. Richard became a solider, and a very good one. His brother utilizes him in the war against the Lancasters, but what is a soldier to do when the war is over? Richard says, in his opening monologue, "Grim-visaged war hath smooth'd his wrinkled front; And now, instead of mounting barded steeds To fright the souls of fearful adversaries, He capers nimbly in a lady's chamber To the lascivious pleasing of a lute." Soldiers, after war, return to their lovers, but what can Richard do, with no woman to love him? He continues the war, killing his way to the throne. Like the attack dog who turns on its trainer, Richard kills even those to whom he was once loyal, because that is all that he knows: how to be a soldier.
Richard is a very complex character and I think that anyone classifying him as simply a villain is missing out on large portions of what makes him who he is. None of this excuses the evils that he has done, the murders he has committed or commissioned, but it helps, in part to understand him. I am not a part of the Richard III Society, which seeks to right the wrongs that have been perpetrated against Richard, correcting the rumors, but I do believe that there is more to him than only his evilness.