A slip clutch functions as overload protection, like a shear pin. If too sharp or extreme of a load is placed onto the PTO drive, the clutch slips, protecting the driveline of the tractor and/or implement from spikes in force that may break something. On a tiller, a large rock, log, or other object may get caught in the tines suddenly, and rather than breaking something on the tiller or tractor, the clutch slips.
An overrun clutch prevents the tractor being propelled forward by power from the implement. Especially with implements that have lots of rotating mass (Mowers, hay rakes, etc) there is a lot of momentum built up in the rotating assembly. Depressing the clutch disconnects the engine from the transmission, but the implement is still fastened directly to the transmission. This means the tractor will be driven forward for quite some distance, with no way for the operator to cut the power to the wheels.
The overrunning clutch is a one way ratchet that keeps the implement from spinning the tractor's PTO shaft and stops the issue of the implement driving the tractor. It's a serious improvement in safety, as well as usefulness of the machine, too. I universally recommend an overrunning clutch for people whose tractors don't have one internally if they are mowing or doing similar things.