Loosely, old; a distinction isn't always made between books that are out of print, books that are rare, and books that are simply secondhand, but the use of “antiquarian” implies that they are collectible. The antiquarian work may be acquired purely as an object of beauty, while the secondhand book may be bought for the pleasure of reading, regardless of its looks.

A collector of old, rare, out-of-print books.

an expert or collector of antiquities

Of old, rare books, or one who deals in them.

Refers to collectible books rather than used books, suggests age or rarity.

'Antiquarian' is a general word for someone, usually from the 18th and 19th century, with an interest in old objects and sites.

Old and/or rare books, or a dealer of same.

Older, more collectable books, rare, or out-of-print