On the contrary, I'd argue that migraines are probably much more common than diagnosed, rather than the other way around. Migraines, much like seizures, vary in both symptoms and severity.
Not my area of expertise, but anecdatally, everyone that I know, that has suffered from diagnosed migraines, has had really crippling symptoms. They seem to be fairly universally severe. I have had headaches all my life (including ones related to a brain tumor, back in the 1990s. The migraines don’t seem to be related to that tumor, which was treated with surgery). In my personal experience, the comparison is night and day. There’s a clear difference.
Basically, a migraine is a “day-ending” event. In my case, I’m fortunate that I can still get stuff done in the morning, but after lunch, the day’s pretty much a write-off.
I’m really grateful that they are so rare (I’ve had three full-term, and one “aborted” one, in the last 30 years). My mother used to get one or two a month, and her day ended fairly early. When I was a teenager, I got them more frequently.