Remote code execution is the process of running arbitrary code on a device over some type of network. The code can either be malicious, such as a code injection on a website, or voluntary, such as with Java Remote Method Invocation.
Remote code execution is the process of running arbitrary code on a device over some type of network. A specific instance of arbitrary code execution, but done on a remote system.
The code does not need to be malicious, as there are technologies that facilitate executing code remotely on a system, such as Java's Remote Method Invocation.
One can argue that any type of access call to a service or website results in remote code execution, but its rarely referred to as that.