A line of credit is similar to a credit card in that it is a flexible borrowing solution. You can draw on this revolving loan by writing a check. You are can also borrow any part of your credit line again once you have repaid it. There are no payments until you use your line.
With a personal loan, you get the whole loan when you're approved and you start paying interest right after on the full amount. You have a schedule of payments that will get smaller until the loan is paid off.