The UHF connector is by far the most popular type used in Amateur Radio. The UHF male (plug) is known as "PL-259" and the female (jack) is known as "SO-239." Typically used in applications to ~400MHz.
FME Adapters are used in applications such as WI-FI, mobile antennas, and others up to ~2 GHz. FME Adapters are routinely misidentified as "mini-UHF". They are similar in appearance, but there are differences. One telling sign between FME and mini-UHF is that the FME male is usually what is installed in equipment and the FME female connectors is what is on the end of coaxial cables on most commercial antennas that use FME as their connection type.