In reply to Fraser:
Yes, the non-pointy side is where the difference is. Unless you are doing pure ice climbing, in which case there may be only the pointy side, for example the Grivel Quantum Race
http://4.bp.blogspot.com/-U3nBIXcd-c4/TzoNmXr0AbI/AAAAAAAAAoQ/4jDvKgvPiC8/s...
But for most climbing, you have an adze on one tool and a hammer on the other.
Both of these can be used for mixed climbing where you place them into a crack, often torquing the tool to provide secure grip. The different head shapes give you more options for placements.
But the main difference is you can use the hammer as a hammer, usually for bashing gear in. This may be the pick of your other tool (or a warthog or a bulldog) into frozen turf, or a nut into a crack and you want to make sure there is no ice, or perhaps you are hammering a peg in.
You use the adze as an adze primarily for digging. This may be to dig a trench for planting an axe for a belay anchor, or to clear snow off the rock to use rock pro, or to dig a bucket seat belay, or to dig a wee shelter into the side of a snowbank so you can eat your lunch out of the wind. You can sometimes use the adze as a climbing tool when you are ascending snow that is too soft to take a pick, but this can be scary (because the snow is often dodgy when you need to do this...)
Hope this helps.
Oh, and
http://www.needlesports.com/imagecache/d5a5042f-3477-429d-8228-9f9900e76501... shows a pair of ice tools with the adze tool above the hammer.
