It’s not really rare, plenty of companies in the US use employment contracts. But a majority don’t, not in the European sense. Technically there is always a contract between any two parties who are cooperating; it doesn’t have to be formalized in any particular way as long as the cooperating parties have a common understanding of the terms and agree on them.

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.