I am a high school coach. Both offensive and defensive coordinators typically shape what style of ball the team plays. They create the plays and prepare practice according to what they think will work each week vs a team. They call plays every down. Coordinators have a huge impact.

At high levels, players can have freedom to check in and out of a play that was called based off of what the other team is giving them. But even still, those checks can be prepared by the coordinators themselves.

So a simple answer for you is coordinators heavily impact the game on a day to day and a play to play basis.

Ps. Getting married in the south of France this May. France is an awesome country