Typically, for a white-collar job, you'd interview and receive a job offer contingent on background check and verifying previous employment. That offer would have a salary and start date and that's about it. HR might hand you a benefits package at the same time.
Sometime on or before the first day of employment, you'd be asked to sign NDAs, confirm legal eligibly to work, and similar paperwork, but almost never a contract.
Senior leaders often have contracts because their terms are more complicated - golden parachutes, etc.
Employment is "at-will" in most states. Employers are obligated to pay for work performed, but you can be terminated at any time (and you can quit at any time).
Some high-level jobs will also have a written contract but it's not normal for a typical salaried or hourly position, unless there is a union involved.
I'm very confident that most people have to a sign a piece of paper listing their pay etc on them before beginning their job.
For at will employment they can change your pay at any time. You're also free to leave at any time of course.
There must be something that both are signing right? With pay rate, hours and benefits written down.