What is the difference between coding and programming? I honestly don’t know much about either and a quick google search didn’t clear it up. If opinions vary, please keep it civilized. 
“Coding” is the process of writing the actual code.
However, people usually just use them interchangeably.
To me there is no difference. At best there is a slight connotation for coding being less structured / preplanned.
I’m a software engineer myself and I just use them interchangeably. Due note that I feel that “programming” is more formal than “coding”, and I also believe that more lay man people would understand what you were referring to more if you used “programming” rather than using “coding”.
I tend to think to think of them as different terms but agree with the above, they are used interchangeably these days, I’ve even used them interchangeably, depending on who I’m talking to. The difference to me is more along the lines of the person doing the programming or coding and what they know.
A Programmer takes into account all the different aspects of the program and how it interacts with the operating system, hardware, other software and even the end-user. There is planning, research, writing, etc. Programmers have gone to school and have a degree in Computer Science, generally. They might be an expert in one particular language (like C++) but often know several.
A Coder is usually someone who taught themselves. A lot of “hackers” or “script-kiddies” fall into this category. People who know how to write code but rarely understand the why or the how behind it. They know how to do some things and could probably write a little program, but could never write a professional program because their knowledge is too limited. They are often only good with a few scripting languages or one particular programming language.
I would consider myself a coder and not a programmer. I could never get a job as a programmer but I can write scripts and small utilities that can automate an entire network.
These are just my opinions but I’ve worked in computers for almost twenty years and this is what it has come to mean to me.
Whenever I see ‘Coding’ I don’t think of anything very much close to Programming. I guess I’ve just been conditioned as such. Instead, I envision Matrix Encoding/Decoding or some other forms of encoding, like Hamming Codes. So coding in the mathematical sense, I guess. But I suppose that’s not what you’re referring to. As fearedbliss and LordCaric mentioned, I think there’s an implied formality to Programming that isn’t there with Coding, but generally speaking its fine to use them interchangeably.
What really gets to me about the overall subject is Programming vs. Computer Science; feels like everyone outside Computer Science doesn’t fully grasp the difference - my relatives included.
+1 for Rhis’ response, as well as Ceno’s. It’s a pretty catch-all sort of phrase.
I’ll also add that in my own field of work “programming” has an additional sub-meaning that entails delivering compiled code (firmware, usually) to end target hardware.