Are there distinguishing features between menstrual migraines and migraines that occur at other times?

No. Menstrual migraines can have any symptoms of any migraines, it just happens that the migraine is triggered and associated with the menstrual cycle.
Yes. Menstural migraines are closely related to a woman's menses-occurring reliably immediately preceding, during or immediately after the period. In those with pure menstrual migraine that will be the only time in a month they get a migraine.