The left side one is a soil aerator. The star spokes should be straightened. The right tool is for picking out weeds on a sowed bed. You can use tools for loads of other jobs though.

Hi Steve, they,re both hand tillers, one you use as you would a hoe, only just dragging it through the soil, the other one is a cylinder one which you just drag through the soil, {or push if you,re feeling energetic, lol } Derek.

you can get different length of handles too. I have a short handle for the tool on the right of your picture so i can get in the beds easily.

I have the one on the right, I call it the claw. I don't have a long handle for mine, and its been used for all sorts over the years - 2 years ago, the chap who was taking out the old fence and replacing with new borrowed my claw to scrape out compacted soil round the concrete at the base of the old posts - when he returned it, he said he'd have been unable to do the job without it. So its uses are many and varied, I've found it invaluable over the years, very tough little tool.

The one on the right is a cultivator, similar to the more common one with a short handle. The one on the left is also a cultivator, and is supposed to work like a hand-powered rototiller. A similar one is sold in the U.S. as the "Garden Weasel".