mobile game; social game
Refers to online, free-to-play mobile games with social features, often abbreviated as ソシャゲ.
See also: ソシャゲ
I recently started a new mobile game.
The appeal of social games is that you can play with friends.
social network game
Dated abbreviation for browser-based social network games, now largely replaced by the broader sense 1.
See also: ソシャゲ
Back then, social network games were mostly played in browsers.