The two are not the same. A book can stay a first edition through many printings, so collectors look for evidence of the first press run. The most common indicator is the number line on the copyright page: a sequence containing a 1, such as '10 9 8 7 6 5 4 3 2 1', signals a first printing. Some publishers instead print 'First Edition' or 'First Printing' outright.
At library book sales, first printings hide in plain sight because volunteers sort by subject and condition, not by copyright page. Check the copyright page on any hardcover by a well-known author, especially debut novels and books that later won awards.
Condition drives the money here more than scarcity. A first printing with a price-clipped or missing dust jacket loses most of its premium, and an ex-library first is worth a small fraction of a clean collector copy.