desert vs piece of ground

desert and piece of ground both are nouns.

Word	Noun	Adjective	Verb	Adverb
desert	Yes	No	Yes	No
piece of ground	Yes	No	No	No

As nouns, piece of ground is a hypernym of desert; that is, piece of ground is a word with a broader meaning than desert:

Other hypernyms of desert include biome, parcel, parcel of land, piece of land, tract.

desert (noun)	piece of ground (noun)
arid land with little or no vegetation	an extended area of land
(usually plural) a person's deservingness of or entitlement to reward or punishment

desert (verb)	piece of ground (verb)
leave someone who needs or counts on you; leave in the lurch
leave behind
desert (a cause, a country or an army), often in order to join the opposing cause, country, or army