There have been a lot of threads on this in the past, so this is the "short answer".

The obvious answer is that a ringed engine has a piston ring, while a non-ringed engine doesn't.

Most (but not all) non-ringed engines are of ABC or ABN construction (both of which I'll just call ABC).

ABC engines are broken in differently than ringed or some other construction types.

Ringed engines can last longer than ABC types, and are usually more tolerate of dusty envrionments. ABC engines usually produce a slightly higher RPM than a ringed engine. (I don't know if anyone still does, but years ago, you could get the same engine from OS and some others in ringed and ABC variants. The ABC type usually put out a tad more power, and was a tad more expensive. Which is funny, since ABC engines are actually less costly to make than ringed engines, though that might not have been the case then).

However, the bottom line is that for the most part, for 99% of flyers, there is little or no real world difference between the types in day-to-day flying, and there are a bunch of different types and configurations out there, more than ringed/non-ringed would indicate.