desert boot vs half boot

desert boot and half boot both are nouns.

Word	Noun	Adjective	Verb	Adverb
desert boot	Yes	No	No	No
half boot	Yes	No	No	No

As nouns, desert boot and half boot are synonyms defined as:

Other synonyms of desert boot include buskin, combat boot, top boot.

desert boot (noun)	half boot (noun)
a boot reaching halfway up to the knee	a boot reaching halfway up to the knee