Programming refers to the act of writing a program for a computer to follow.
Coding refers to the act of writing code for a computer.
Edit: The definitions are not commonly used this way and in fact I've heard other people even give opposite definitions to what correponds to which word.
Hate to break it to you, but all definitions are made up. The question is whether or not the distinction is useful or not. In my opinion, it seems useful to distinguish between understanding oriented tasks and goal oriented tasks.
Programming refers to the act of writing a program for a computer to follow.
Coding refers to the act of writing code for a computer.
Edit: The definitions are not commonly used this way and in fact I've heard other people even give opposite definitions to what correponds to which word.