This is one of those little things that bothers me, but only in a small way. I myself will default to rogue-like at times even if the game is technically a rogue-lite, but I do feel the differences are important.
Caveat: Everything here is my subjective opinion, and the games I choose as examples may fall elsewhere if someone else would make a list. I'm going to pick games that come to mind and I have played, even if there might be better options out there.
Lets crib from the Mohs scale shall we? This is Rine's scale of Rogue-like hardness. 0 is more rogue-like, higher is less and less like Rogue.
Common definition of Rogue-like
So for those of you who don't know. Rogue-like is a descriptor of a type of game that is...like Rogue. Rogue-likes are games where dying and starting over is part of the process. This means some sort of progress loss, and might require several from-start retries before someone finally finishes the game. What you carry over from try to try varies wildly between the different ratings of the scale. Often the games include some amount of randomness, varying from levels layouts, item drops, enemy placements, or even having to identify items which change descriptions each time.
0: Pure Rogue-Likes
Probably the easiest category to define. If a Rogue-like is a zero on the scale, it is pure rogue-like. Every time you play the game, you start with the exact same sort of things you started with the first time. Dying in the game gives you zero benefit, and the only difference a long-term player and a new one have is the long-term player has more experience. Finishing these games is entirely up to your skill with the game itself.
Notable examples:
- Tales of Maj'Eyal
- Nethack
- Rogue
- ADOM
- Dungeons of Dredmor
1: Choices, but no power
Here is where Rogue-likes start to keep track of your progress between games. These sort of games unlock new starting options when you achieve certain in-game goals, though the options are not inherently more powerful than other options. Some of these might be game modes, alternate builds, classes, or the like. The only thing that makes these games easier on replay is the player might unlock a class/setup that fits their playstyle better, thus making it easier for them.
Notable examples:
- FTL
- Nowhere Prophet
- Jupiter Hell / DoomRL
- Nuclear Throne
2: Unlocks for new runs
These Rogue-likes tend to be card or similar based, but action-styled games also can fit. Essentially, these rogue-likes lean more into the randomness of each run, whether card drops or item pick ups, and notably achieving certain goals during runs unlock more cards/items. If they are not inherently more powerful the might actually fit in the 1 Scale games, but usually these are just better items/cards than you might have had before. You still start at the same power level, but there are more chances to get much stronger. Easy way to explain it is: Are there builds you can only do once you unlock certain items that are considered superior? The game goes here, especially if you can get the items at the start.
Notable examples:
- Binding of Isaac
- Banners of Ruin
- Slay the Spire
- Downwell
3: Now with upgrades
Here is where I would change the lingo from Rogue-like to Rogue-lite. These are games that introduce direct upgrades into the gameplay, but in a limited way. These will obviously make further runs easier, but tend to avoid direct stat increases. Usually these are limited by slot options, or unlocks being better starting gear. The game might have a +10% Damage unlock, but you can only include so many unlocks, so unlocking other options isn't just a straight upgrade. This can often include 'Banishment', preventing items/drops you don't like from showing up and improving your chances.
Notable examples:
- Curse of the Dead Gods
- 20XX
- Dead Cells
- Iris and the Giant
4: Straight up buying power
At this point, the games are basically designed to not be finished on the first run. It is possible, but these games have intricate upgrade systems, along with straight up number boosting. There is likely a damage/defense/hit point stat to be upgraded, along with other more nuanced things. You are expected to get further, earn more of the resources, come back, upgrade, and repeat.
Notable examples:
- Immortal Redneck
- Neon Chrome
- Rogue Legacy
5: Death for Story
At the final hardness level, dying is part of the game's story. If you did manage to finish the game in your first run, you would actually miss a large part of what the game has to offer, and it may be actually impossible due to story limitations. The game will get easier each run, more story will show itself, and eventually you will finish the game. Finishing the game might just unlock more story to be seen in even more runs.
Notable examples:
- Loop Hero
- Hades
- Children of Mora
- Void Bastards