As others have said, sharp sand is actually crushed rock, and has particles of various size in. I've recently been reading about soil & soil improvers, as I'd like to start growing some veg next year, and autumn & winter is the perfect time for reading & planning what to do next year. Lots of books say adding sand to clay soil helps, as it makes the soil more open, and helps to prevent a 'crust' forming when the soil starts to dry out, thus aiding drainage (otherwise the water just runs off the crust, and does not penetrate to the roots). Adding any organic matter, and digging, helps to aid drainage, as it makes the soil more porous and opens up the structure.
Sand DOES improve drainage, this is why you are advised to brush sand into your lawn every autumn, after removing dead grass by raking, and putting some holes in (or de-thatching and aerating to give them their Sunday names).
If you look at a bag of sharp sand and a bag of horticultural grit, there's not a great deal of difference - apart from the price, that is!