It's called
Mittelschmerz (literally, middle pain) and I get it something fierce. It will last for around 2-4 hours, sometimes longer, and doesn't respond well to Aleve, unlike regular cramping.
I thought that when I had kidney stones that it was this at first, but then I remembered I was on the Ring and didn't ovulate.
It's the only downside to my current method (Mirena IUD); I ovulate again, so once a month have to put up with the pain. But at least I don't have a period anymore, so it's a tradeoff.