I've never heard programming and coding distinguished in that way. Writing a program is programming...or coding. When you mix in things like design, test, requirements, etc. it becomes software engineering. At least based on how I've heard these terms used in the past. But then I think "coding" is really a newer term than "programming".

!hivebits

My first programming class was in high school starting in 1989. We were programming in BASIC on TRS-80 Model 3s and 4s. Ancient even then. But yeah, i would say we were problem solving. Later on in high school I had a programming class in Pascal using IBM PCs. That was definitely more just coding I would say based on this definition. But then the teacher of that class was the coach...and an ass.