Most literally, first printing concerns the first print run of a book off the press, and is often used in describing works of fiction. A later run or printing is could still be the same book in terms of look and content, but just printed later. However, some folks do not make this distinction, and call a first printing a first edition and vice versa. Just remember that first editions can have more than one printing, so if you want a copy of the very first printing of a book, especially a nonfiction book, be careful. State - This is another complicated issue in book collecting.
State refers to small changes in a book made by the printer in the middle of a print run.
These books were put on sale at the same time, with small internal differences like corrections, additions, subtractions, etc. Some times number of volumes of the original state of a book is very small, and becomes a great deal more collectible due to its rarity. Even if a book is a first edition and in great condition, its scarcity is very important. The newest book by a popular mystery writer may have a first edition print run of hundreds of thousands of copies. Sometimes, a book will be printed in a very small limited edition, usually under 1500 copies.