Every employee has a contract; it may be verbal and it may be renewed from day to day or moment to moment. But an agreement to forfeit one's leisure time in lieu of a settled amount of remuneration is a contract.
Sorry you are mistaken. ...what you described is a “agreement”....not a contract...
When you sign your employment application...you are agreeing to the terms of employment. ...
A contract is an entirely different legal document...
I also would add any company worth their salt..has a disclaimer somewhere in their hiring paperwork that the employment application is not a contract....