softball game vs softball

softball game and softball both are nouns.

Word	Noun	Adjective	Verb	Adverb
softball game	Yes	No	No	No
softball	Yes	No	No	No

As nouns, softball game and softball are synonyms defined as:

softball game and softball: a game closely resembling baseball that is played on a smaller diamond and with a ball that is larger

softball game (noun)	softball (noun)
a game closely resembling baseball that is played on a smaller diamond and with a ball that is larger	a game closely resembling baseball that is played on a smaller diamond and with a ball that is larger
	ball used in playing softball