I have heard about things like \"C Runtime\", \"Visual C++ 2008 Runtime\", \".NET Common Language Runtime\", etc.
Runtime describes software/instructions that are executed while your program is running, especially those instructions that you did not write explicitly, but are necessary for the proper execution of your code.
Low-level languages like C have very small (if any) runtime. More complex languages like Objective-C, which allows for dynamic message passing, have a much more extensive runtime.
You are correct that runtime code is library code, but library code is a more general term, describing the code produced by any library. Runtime code is specifically the code required to implement the features of the language itself.
a runtime could denote the current phase of program life (runtime / compile time / load time / link time) or it could mean a runtime library, which form the basic low level actions that interface with the execution environment. or it could mean a runtime system, which is the same as an execution environment.
in the case of C programs, the runtime is the code that sets up the stack, the heap etc. which a requirement expected by the C environment. it essentially sets up the environment that is promised by the language. (it could have a runtime library component, crt0.lib or something like that in case of C)