last half vs second half

last half and second half both are nouns.

Word	Noun	Adjective	Verb	Adverb
last half	Yes	No	No	No
second half	Yes	No	No	No

As nouns, last half and second half are synonyms defined as:

last half (noun)	second half (noun)
the second of two halves of play	the second of two halves of play