What is the grammatical term for "Defense Minister" vs "Minister of Defense"?
The -er suffix indicates an agent noun. The -ing suffix indicates a gerund. Using a noun to modify another noun is noun adjunct. While "minister" ends with "-er", there is no word "minist", so this is an odd case where there's a word that looks like an agent noun, but doesn't follow the same pattern of being a verb plus -er. It can be considered a noun form of "administer", but that already has -er.