I was told growing up that migraines were different from headaches, although it looks like now migraines are sometimes called "migraine headaches". The distinction mattered because the treatment for migraines (things that caused blood vessel constriction, like caffeine) and for other types of headaches (things that caused blood vessel dilation) were opposites, so if you took the wrong medicine it could make your head hurt more. For a first time migraine sufferer, the difference might not be obvious.
That said, I'm not sure how either could be mistaken for neck muscle pain.
Yes, migraines are weird. I am kind of lucky in that mine are neither frequent nor as bad as those by others. For me it manifests as a headache in a distinct spot 9 out of 10 times and I get very sensitive to sound and light (auras are usually very light or not there at all, no nausea or puking). The good thing is that a) I can just take a mild dose of ibuprofen and b) go into a dark, silent room and sleep it off most of the time, on the other hand when I tried triptanes? that didn't work at all. Also I only have a few every year and not multiple times per month like when I was a kid or teenager.
For me the difference is usually easy. If it's a headache-headache, it's annoying and you can function (even if it hurts). If it's a migraine then I simply can't work or do any fun thing anymore, not even watching something or reading.
That said, I'm not sure how either could be mistaken for neck muscle pain.