fireball vs ball of fire

fireball and ball of fire both are nouns.

Word	Noun	Adjective	Verb	Adverb
fireball	Yes	No	No	No
ball of fire	Yes	No	No	No

As nouns, fireball and ball of fire are synonyms defined as:

Other synonyms of fireball include human dynamo, powerhouse.

fireball (noun)	ball of fire (noun)
the luminous center of a nuclear explosion	someone whose career progresses rapidly
a ball of fire (such as the sun or a ball-shaped discharge of lightning)	a highly energetic and indefatigable person
a highly energetic and indefatigable person
an especially luminous meteor (sometimes exploding)