Net 60 payment terms mean the customer must pay the full invoice amount within 60 days. Unless your terms say otherwise, the 60 days are calendar days counted from the invoice date, so an invoice dated March 10 on Net 60 is due on May 9. Net 15 works the same way over 15 days: the same invoice would be due on March 25.
"Net" refers to the amount, not the timing. It means the full invoice total, with no discount for paying early. The number after it is how many days the customer has.
Net 60 is usually something a supplier accepts because a larger customer asks for it. Net 15 is something you choose, to get paid sooner on smaller or riskier work.