Being a long term patient of neurologists (migraines, seizures) and having a wife who works in neurology I tend to believe the doctor she worked with who stated that once you have migraines, all headaches are a migraine clinically. They’re just more or lwwa debilitating based on severity.
Interesting, I’ve always categorized them by whether they go away from standard painkillers or if I need to use rizatriptan. Migraines are much more frequent for me than normal headaches but I still do have ones that go away when I take some tylenol or ibuprofen. I’ve been lucky so far that my migraines almost always go away after 1 rizatriptan, and I’ve never had one make it past a second one.