To move or push something, you "exert" a "force". Exertion is the effort, and force is the result.

We often use TO FORCE when it's against somebody's will. Covid forced us to stay indoors. My teacher forced me to write 3 assignments. Etc EXERT is used more to show mental or physical effort. I was very tired yesterday but I exerted myself to complete all my lessons. Try and exert yourself to find a solution. A parent exerts their authority on their children.

to force - deliberately to exert - unintentionally to force a situation / to exert oneself.