Rogue for the rogue mechanic.
Progressing in a game as far as you can until you die, then using some form of enhancement mechanic be harder faster better or stronger to go again.
Funny enough, Rogue doesn't have a set of permanent enhancement for a wider meta game. In Rogue you start over from scratch always and every time. That's the difference between a roguelike and a rogue liTe game. Binding of Isaac and Spelunky are roguelike. You die, you start over from scratch. Hades and Slay the spyre are rogue lite. Every run gives permanent enhancements that change the next runs, so each time you start slightly different or progressively better.
Hades, yes. That's a premier Roguelite with meaningful meta progression.
Slay the Spire is fuzzy on that point. I would not recommend it to someone looking for a Roguelite. It straddles the line in that it has very limited meta progression which is quickly exhausted and basically works as a tutorial. Once you've maxed out the card unlocks for each character it plays with the same feel as a Roguelike game. It's still not a pure a Roguelike since the starting boon choice and the card swap event allow some minor meta-influence between runs, but there's no more meta-progression.
A roguelite is ostensibly something that has enough features of a roguelike to be noted, but not enough to be considered one. And I'd argue there is way more to what makes a roguelike than permadeath with no meta progression.
Also Slay the Spire has less meta progression than Issac. Hades is in a whole nother ball park.
Be careful; you're stepping into a holy war. There are some who stick to "the Berlin Interpretation", where there are far more criteria to what makes a roguelike, and from my perspective, it makes those games so close to Rogue that it's not worth giving it its own genre, plus this classification came out just before Spelunky ruined it. Colloquially, you're typically right though. Most will call a game roguelite if your progress gives you upgrades that make the next runs easier, whereas a roguelike may still have unlocks that add more variety or "sidegrades" that are neither better nor worse.
I think the Berlin Interpretation is quite outdated and was not even good at the time, but I will defend it on this one point. It does not provide a threshold for what is and is not a roguelike, the Berlin Interpretation just lists criteria that are important to consider when determining how roguelike something is. The heap paradox is an exercise for the reader.
I’m curious if it’s actually a different one. That’s the biblical “source” but I feel like there was a long gap before the indie scene picked up that theme in droves. I’m now unsure what it was that started that more modern trend.
Rogue was the originator, but NetHack and ADOM did more to popularize Roguelikes than Rogue itself ever managed. NetHack was the first one I ever heard of, and it's the only reason I know Rogue existed in the first place.