Story-Driven
A story, a setting or a journey of a hero. Stories are an approach I prefer much more because mechanics can be derived more easily.
Mechanics
One single mechanics or a set of mechanics is thought of. They might be something entirely new, or a combination of existing ones.
It all starts with an idea...
AND THEN TURNS INTO A GAME.
Conceptualization
Design Fixture
Prototyping
Feedback
Deliverable
Think about a concept, it maybe a story or a set of game mechanics. Then expand on it to make a full working concept which is possible to do.
Now that a concept is ready, a Game Design Document is made to fix the design and the vision of the game. Other documents such as art asset list, level design document and more are also made.
Take the said design and prototype it. Maybe in Unity or Construct, just to get a feel if it's working or not.
Test the mechanics/level to get feedback. It might be technical or personal, but if something isn't working, go back to prototyping and fix it.
Deliver the said content after all the steps.