lust vs sexual desire

lust and sexual desire both are nouns.

Word	Noun	Adjective	Verb	Adverb
lust	Yes	No	Yes	No
sexual desire	Yes	No	No	No

As nouns, sexual desire is a hypernym of lust; that is, sexual desire is a word with a broader meaning than lust:

Other hypernyms of lust include concupiscence, eros, physical attraction.

lust (noun)	sexual desire (noun)
self-indulgent sexual desire (personified as one of the deadly sins)	a desire for sexual intimacy
a strong sexual desire

lust (verb)	sexual desire (verb)
have a craving, appetite, or great desire for