More like valueAt(12, 34) or valueAt(12, 34, 56) depending on if its a 2D or a 3D noise function. I guess there is one dimensional noise but it's not used often in my experience.
"How high should this terrain be?" is probably based on 2D noise.
"Should there be a block here like in Minecraft?" is probably based on 3D noise. (or some complicated 2D noise)
"Should the fifth spawned monster drop loot?" could be based on Random... if you want it repeatable.
Though really the cases for Random are kind of rare. If the player goes left versus right and hits a different monster spawner then "fifth spawned monster" could be something totally different than when you played.
I use regular Random in Mythruna's tree generation but only because I use a statistical distribution for trees/plants instead of a spatial one. (the plan was to always switch to fractal planting patterns later). So I seed the Random object with the seed of that particular "chunk" of the world. Then as I iterate (in consistent order) over the possible tree/plant locations, I check the value of Random() against a set of conditions.
Even if I use a spatial noise-based planting plan, I'd probably skew it by the consistent sequential random values. It turns out that a statistical distribution will produce more interesting results even if they aren't particularly realistic. Sometimes nature doesn't make sense, either.
So it will likely be that I never have code that is purely noise based for tree placement because it would be too uniform. Example: large clump of well spaced trees surrounded by plants/grass in a nice border, etc.. Likely I will use it as an influence on Random... else I will have to layer several fractal octaves onto it before it's useful. (And truthfully, the 'should I plant this here' question has a lot of potential inputs other than a randomization factor.)