And I disagree... A DC 15 lock is more difficult than a DC 10 lock and yet neither is more deadly... There are plenty of examples in D&D where difficulty and deadliness don't equate 1:1.
:sigh: True. A campaign where PCs went around making tough, but perfectly safe, checks to do stuff, instead of getting in life-threatening combats, could still be 'difficult.'
So would one where they're in constant danger of death from overwhelming enemy forces.
The expectation of a D&Der familiar with 1e and/or 5e, is that the game will be way more difficult, in both the 'I'm having difficulty picking this lock' (because my pick-locks 'special' ability is only 25%) and the 'Oh, my god, we're all going to die' (because combat is pretty deadly) sense, early on, and slide more into 'easy mode' as it progresses.
A non-D&Der might expect an introduction to the game to be the easy version. Or not. I haven't been a non-D&Der in a very long time.
I'm pretty sure "level appropriate challenge" === "the game scenarios encountered increase in absolute difficulty to compensate for the relative increase in power level of the PCs."
It means challenging for the level of the party. So, in 3e, a single same-CR critter, in theory. At high level, that'd mean a creature with tons of hps, an AC only the figther could hit consistently, etc...
In 5e BA, it means an encounter of a certain exp budget, with a multiplier for number of foes, that could be a single higher-CR creature or a bunch of lower-CR critters. FWIW.