I think most people don't even know that much, this isn't something that is deeply covered in most intro to bio courses in college; you have to learn a bit about how DNA is packaged and transcribed which you'd get in upper division courses. At least in the field, there is no confusion. Non-DNA inheritance is inheritance of these epigenetic regulatory states in which you've described, but the term used specifically for this is transgenerational inheritance.

We shouldn't assume we know all mechanisms, true. I do believe I've read of RNA changes retained over generations but could be wrong about that.