At the International Roguelike Development Conference 2008 held in Berlin, Germany, players and developers established a definition for roguelikes known as the "Berlin Interpretation".
These guys have extremely strict definitions, which mean that most "rougelike" games are in fact roguelites, if you care about what they think.
There are nine "high value" factors that are more or less a requirement:
Random Environment Generation
Permadeath
Turn-Based
Grid-Based
Non-Modal
Complexity
Resource Management
‘Hack-n-Slash’
Exploration and Discovery
Plus six "low value" factors that are less important:
Single Player Character
Monsters are Similar to Players
Tactical Challenge
ASCII Display
Dungeons
Numbers
There is, as you might expect, a fair bit of controversy about that though.
Yeah, a big shift in the definition happened with the roguelike hype in the 2010s, spearheaded by The Binding of Isaac, FTL etc.. It wasn't as controversial back in 2008.
For all but the most stubborn purists, that definition has sort of retreated to the more specific term "traditional roguelike", letting the roguelike/roguelite distinction be about meta progression.
Although I agree with the author of this article that the terms are somewhat muddied, even in their more generally accepted definitions, by the fact that it's hard to draw the line for when unlockables can be considered "permanent progression".
Although I have many gripes with the terms in general and how they're used, I'm of the opinion that it is clear enough for there to be a distinction; if all of the unlockables in a roguelike game are sidegrades, or merely more options without inherent strength over other options that are unlocked from the start, then it still counts as a roguelike.
Though admittedly, this can be a bit blurry too.. it would be pretty easy to argue that some unlockables in games like these are more powerful than other options, especially because it's very hard to put an objective "power level" on an item in a roguelike. Also, one could argue that merely having more options makes the game easier, thus it counts as permanent upward progression.
Yet regardless, the article's attempt to coin the term "rogues" as the all-encompassing sub-genre/game mechanic name absolutely won't catch on, and the differentiation between the terms does have a lot of value for people trying to determine whether or not they will enjoy a particular game, even if the line can be a little blurry.
Here's a relevant video that I enjoyed by Game Maker's Toolkit that focuses on the main mechanical differences between the two designs, from a very broad and practical overview, definitely recommend watching it if you're interested in this sort of thing
Here's another tangentially related video by Chariot Rider about roguelike progression in particular, which I also found interesting, although less relevant to this discussion
Even more tangentially, here's a fun video by Lextorias about confusing or controversial game genres (well.. game genres in general) and it has a big section about the distinction between roguelikes and roguelites
I don't think I've seen that particular video, but just wanted to chime in with a general endorsement of Game Makers Toolkit. Absolutely superb channel, highly recommended not just for game makers but for anyone interested in the mechanics and general nuts-and-bolts of gaming.
To be fair most of the confusion stems from just the stupidity of the word rogue-lite. I also believe that if you insist on using the words interchangeably - that's fine as long as you correctly establish the context. Like first you say you're going to talk about Hades and Dead Cells and then you bring the R-word into it. I personally get confused when I see a video on YT saying best upcoming roguelikes and there isn't anything resembling Rogue on it at all and the author seems to be completely unaware of the existence of a whole genre. Happens more than I'd like to admit.
Roguelike is getting a random brand new dessert from a wide variety of desserts and not knowing whether you will get the same one next time. Roguelite is getting a vanilla cone ice cream, and each time you get the same vanilla cone ice cream but more options for toppings.
That's how meanings have shifted. Originally roguelite meant anything that borrows stuff from roguelikes while not playing like the original rogue.
Stuff like Nethack, Dungeon Crawl (Stone Soup), Pixel Dungeon, ADOM, Mystery Dungeon,... were the true roguelikes. If you ask the purists, they'll probably throw the freaking Berlin Interpretation at you.
The Binding of Isaac muddled the popular definition of roguelike (because frankly, it was not on the radar of many people before that).
Now everything using procedural generation and maybe a hint of permadeath gets to be called roguelike.
Rogue-lites are usually games with only a few elements of Rogue. Mostly what differentiates them is that you can often unlock things that persist between lives, unlike a true Roguelike where you start over 100% from scratch with each character/new game.
Pixel Dungeon is a Roguelike. Hades is a Rouge-lite.