Shelf is the noun, the flat board you put books on. Shelve is the verb, meaning to put something on a shelf, or, figuratively, to put a plan aside for later. If you can put an -s or the on the word, it is shelf; if you are doing an action, it is shelve.
The core difference
Shelf is the object you place things on; shelve is the act of placing them there, literally or figuratively.
- shelf — a flat board fixed to a wall or cabinet, used for holding objects: she lined the top shelf with her favourite novels.
- shelve — to place something on a shelf, or to furnish a place with shelves: he shelved the new arrivals before closing the shop.
- shelf — also a ledge that juts out, as underwater rock or ice: the continental shelf drops away into deep ocean.
How to tell them apart
Shelf is the older word, going back to Old English for a ledge or flat surface. Shelve is a later verb formed from it, and it kept a literal sense, to put something on a shelf or to fit a room with shelves, alongside a figurative one that is now extremely common: to shelve a plan means to set it aside for the time being, as though putting it out of sight on a shelf.
Watch the plural too. The plural of shelf is shelves, not shelfs, and it is this plural that shelve was originally formed from.