【Desire】 , 【wish】 , 【want】 , 【crave】 , 【covet】 mean having a longing for something.

【Desire】 , 【wish】 , and 【want】 are often used with identical intent though in such situations (usually everyday ones) that the degree of intensity of longing or need is not at issue.

In such use 【desire】 is often felt as more formal and dignified, and it may even be decidedly pompous in effect.

【Desire】 in more general use, however, emphasizes the strength or ardor of feeling and often implies strong intention or aim.

【Wish】 is less strong, often suggesting a not usually intense longing for an object unattained, unattainable, or questionably attainable.

【Want】 (see also LACK) is a less formal term than 【wish】  and so is often interchangeable with it in situations where dignity of the subject or respectfulness is not at issue, though generally 【want】 implies that the longing is for something the attainment of which would fill a real need and which is actively hoped for.

【Crave】 implies strongly the force of physical or mental appetite or need (as of hunger, thirst, love, or ambition).

【Covet】 implies a strong, eager  【desire】 , often inordinate and envious and often for what belongs to another.