professional golf vs golf game

professional golf and golf game both are nouns.

Word	Noun	Adjective	Verb	Adverb
professional golf	Yes	No	No	No
golf game	Yes	No	No	No

As nouns, golf game is a hypernym of professional golf; that is, golf game is a word with a broader meaning than professional golf:

professional golf: playing golf for money
golf game: a game played on a large open course with 9 or 18 holes; the object is use as few strokes as possible in playing all the holes

Other hypernyms of professional golf include sport, golf.

professional golf (noun)	golf game (noun)
playing golf for money	a game played on a large open course with 9 or 18 holes; the object is use as few strokes as possible in playing all the holes