That's not quite true. EDSM shows if you're the first person to discover the object and submit to EDSM; it doesn't show the game's own record, and can't take into account objects discovered by people not using EDSM.
Although, if you're more than a few thousand ly from civilisation, those two things are almost always the same.
I thought you could track your own discoveries if you uploaded to EDSM? I did upload for a bit, but don't usually. I liked the fact that I could track where I'd been. It doesn't help you find other people's first discoveries though.