In the C and C++ languages there's a thing called a "freestanding" implementation. This is roughly analogous to Rust's nostd.
In C the freestanding environment doesn't provide any concrete features, you don't get any functions at all, you can get a bunch of useful constants such as the value of Pi or the maximum value that will fit in an unsigned integer, some typedefs, that's about it. Concrete stuff from the "C standard library" is not available, for example it does not provide any sort of in-place sort algorithm, or a way to compare whether two things are the same (if they fit in a primitive you can use the equality operator)
In C++ there are concrete functions provided by the language standard in freestanding mode. These, together with definitions for types etc. form the freestanding version of the "standard library" in C++. There's a long period where this was basically untended, it wasn't removed but it also wasn't tracking new features or feedback. In the last few C++ versions that improved, but even if you have a new enough compiler and it's fully compliant (most are not) there's still not always a rhyme or reason to what is or is not available.
In Rust it's really easy. You always have core, if you've got a heap allocator of some sort you can have alloc, and if there's a whole operating system it provides std.
In most cases a whole type lives entirely in one of those modules, Duration for example lives in core. Maybe your $5 device has no idea which year this is, let alone day but it does definitely know 60 seconds is a minute.
But in some cases modules extend a type. For example arrays exist in core of course - an array of sixty Doodads where Doodads claim to be Totally Ordered, can just be unstably sorted, that works. But, what if we want a stable sort, so that if two equal Doodads were arranged A, B they are not reversed B, A ? Well Rust's core module doesn't provide a stable sort, the stable sort provided uses an allocation and so the entire function you need just doesn't exist unless you've got allocators.