What is "runtime"?
Runtime is a general term that refers to any library, framework, or platform that your code runs on.
The C and C++ runtimes are collections of functions.
The .NET runtime contains an intermediate language interpreter, a garbage collector, and more.
The runtime or execution environment is the part of a language implementation which executes code and is present at run-time; the compile-time part of the implementation is called the translation environment in the C standard.
Examples:
the Java runtime consists of the virtual machine and the standard library
a common C runtime consists of the loader (which is part of the operating system) and the runtime library, which implements the parts of the C language which are not built into the executable by the compiler; in hosted environments, this includes most parts of the standard library
As per Wikipedia: runtime library/run-time system.
In computer programming, a runtime library is a special program library used by a compiler, to implement functions built into a programming language, during the runtime (execution) of a computer program. This often includes functions for input and output, or for memory management.
A run-time system (also called runtime system or just runtime) is software designed to support the execution of computer programs written in some computer language. The run-time system contains implementations of basic low-level commands and may also implement higher-level commands and may support type checking, debugging, and even code generation and optimization. Some services of the run-time system are accessible to the programmer through an application programming interface, but other services (such as task scheduling and resource management) may be inaccessible.
Re: your edit, "runtime" and "runtime library" are two different names for the same thing.
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.