MMCX connectors provide a stronger connection to antennas than U.FL connectors (less signal loss) and MMCX is less fragile than U.FL: UFL connectors are more prone to pop off the miniPCI card.
H.FL is an older connector type that is infrequently used now, but you will find these on minPCI wireless cards from time to time. H.FL looks very much like U.FL and the two are sometimes confused. See the photos above to determine the difference.
U.FL connectors' gender is confusing because a U.FL jack, such as you would find on a miniPCI male wireless card or board is the male U.FL connector. So U.FL gender is an exception to the rule for most other RF connector types, for which "jack" is synonymous with "female connector." See the photo of U.FL male and female: Above at top of page, on left side