I have never seen a paystub or been told what a paystub is.
For each wage payment, I got an "Earning Statement" on https://my.adp.com. Is an earning statement a paystub?
Yes, your earning statement is your paystub.
Back in the olden days*, before direct deposit, your employer would give you a physical check that you had to take to the bank. Your earning statement would be attached to the check, and when you would tear off the paycheck, the earning statement would be left. That's where the name "paystub" comes from.
The earning statement is important, as it shows you how much was withheld in taxes and how much was deducted for other expenses, such as health benefits or retirement savings. When you get your W-2 statement at the end of the year, you can confirm the amounts with the numbers from your earning statements.
* I still get a physical paycheck and stub.
Yes, an earnings statement is a paystub, or pay advice.
It gives an accounting of your pay from the payroll department including salary, vacation, holiday, or sick days. For hourly employees it might include hours at regular pay, overtime at different rates, shift differentials, and tips. It can include bonuses, commissions, and meal allotments. It can include reimbursements for expenses submitted by the employees, and it often includes an accounting of accrued time off that has not yet been paid.
It should list also list money withheld for payroll and income taxes, for medical and other insurance and benefits, for savings plans (as well as a note of matching funds from the employer). It may include deductions for additional PTO purchases. It may include deductions for repayment of loans made by your employer or rent for housing provided by the employer. It may have dues withheld for unions or trade associations. It may have charitable contributions voluntarily withheld to take advantage of charity matching programs.
The detailed account of the monies for that pay period allow employees to verify that their payments were properly processed by the payroll department, and should be carefully examined each pay period.