Blue Prince is a roguelike puzzle masterpiece

> As with other roguelikes, you can unlock persistent upgrades that smooth over repetitive parts of the game.

I think those are called rogue-lites, for the reason that real rogue-likes (e.g. nethack, DCSS) actually wipe out all your progress on each attempt.

At this point, times have shifted, and meta-progression is usually considered an aspect of modern roguelikes. There was a trend of calling them "rogue-lites" but that's faded and now games like ADOM and DCSS are "Classic roguelikes"

It's not a hard and fast rule or anything, just what I've observed in gaming discussions.

Indeed, the distinction used to be useful. But now, it's not useful because honest-to-God roguelikes are just not getting made outside hobby projects. Meanwhile, roguelites have become a core pillar of modern gaming, artistically and commercially. I think calling roguelites roguelikes is perfectly fine. It's simply what the genre became.