Employment contracts in the US are rare.
While US employment is usually at will without a defined contract term, there are mutually enforceable obligations, including some definition of what the employee is obligated to do for the employer and that the employer is obligated to pay the employee at some specified rate assuming the employee's obligations are met. That's a contract. Exactly what the detailed terms are may be difficult to prove absent a single comprehensive written document, but it is a contract.
Really? Does that mean what it say: you get a job and you do not get a written contract?
I don't think, in 38 years of working in 3 different countries, I've ever NOT had a written contract, even for temp or contractor roles. WTAF?
Executives can be an exception.
Exceptional circumstances are an exception.
Increasingly less common union jobs are an exception.
But ‘at will’ is far more common in the US.
Many companies that don’t use formal contracts instead put all the information that is common to all employees into an employee handbook, and the details that are unique to a specific employee into the offer letter. The offer letter given to a new hire has details such as their starting salary and start date, and once they arrive they are given a copy of the handbook and often time to read it and discuss it with a manager. The handbook will explain in detail how promotions happen, the work expected from for various job titles, any rules the employees are expected to follow, etc, etc. Together these form the common understanding that underlies the contract, even if there is never a formal contract signed by both the employer and the employee.
Contractors, on the other hand, always have a formal contract. Often a contractor spends a significant amount of their time negotiating these contracts, especially the scope of work. I should know, I worked as a contractor for many years.