haste vs rushing

haste and rushing both are nouns.

Word	Noun	Adjective	Verb	Adverb
haste	Yes	No	No	No
rushing	Yes	No	No	No

As nouns, haste and rushing are synonyms defined as:

Other synonyms of haste include hurry, rush.

haste (noun)	rushing (noun)
the act of moving hurriedly and in a careless manner	(American football) an attempt to advance the ball by running into the line
overly eager speed (and possible carelessness)	the act of moving hurriedly and in a careless manner
a condition of urgency making it necessary to hurry