As peachey said, they both are different forms of words. So you should rather be comparing DESERTED and DESOLATE. Deserted : 1. abandoned; forsaken: the problems of deserted wives and children. 2. untenanted: without inhabitants: a deserted village; a deserted farmhouse. 3. unfrequented; lonely: The victim was lured to a deserted spot. Desolate : 1. barren or laid waste; devastated: a treeless, desolate landscape. 2. deprived or destitute of inhabitants; deserted; uninhabited. 3. solitary; lonely: a desolate place. 4. having the feeling of being abandoned by friends or by hope; forlorn. 5. dreary; dismal; gloomy: desolate prospects. As you can see, deserted is an adjective that describes something that has been forsaken. It is an effect caused by people not frequenting the place or people being forsaken by others. desolate on the other hand has a dark shade to it. It is dreary and a bad place to be in. It may be caused by people deserting it or some other reasons. It is a place which often feels being stripped of happiness and hope. Desolate is much more negative in meaning than deserted.

Desert is a noun, and desolate is an adjective.

desolate = barren or laid waste; devastated: a treeless, desolate landscape, deprived or destitute of inhabitants; deserted; uninhabited. desert = any area in which few forms of life can exist because of lack of water, permanent frost, or absence of soil, wasteland, or barren wilderness.