I am still a beginner, but after 1 year I'm still not sure about the difference. I've been talking with some citizens from China mainland on the Internet, when I mentioned that I'm learning 國語, I seemed to offend people, and it sparked some rows in comment sections before.
I have lots of confusion. Now I know 國語 means "the national language", and 普通话 is "the common language", and is a standard. I'm learning based on Taiwanese materials, and they refer to 國語 as the language there, which is for all intents and purposes the same as 普通話.
I'm unsure why it causes so much fuss. Is 國語 an unpopular term outside of Taiwan? If so it makes sense where confusion comes from.
My teachers and materials seem to make no real distinction, and both terms are even interchangeable from how I've been taught. I would love to have this cleared up.