desire - the feeling that accompanies an unsatisfied state. I think desire has a stronger meaning than wish. Both desire and wish mean "want", but desire is much closely related to human, such as sexual desire, or even greed or cravings. We don't say sexual wish, do we? On the otherhand, Wish is widely used as a polite substitute for want with infinitives: Do you wish to sit at a table on the terrace? Anyone who wishes to may leave now. This usage is appropriate for formal style, where it is natural to treat the desires of others with exaggerated deference. The corresponding use of wish with a noun-phrase object is less frequent: Anyone who wishes an aisle seat should see an attendant. Both usages are likely to sound stilted in informal style, however, and want may be substituted for wish.·A traditional rule requires the use of were rather than was in a contrary-to-fact statement that follows wish: I wish I were (not was) lighter on my feet. While many people continue to insist on upholding this rule, the indicative was in such clauses can be found in the works of many well-known writers.

http://www.thefreedictionary.com/desire
http://www.thefreedictionary.com/wish