The UHF connection 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.
Type C connections use 2x stud, bayonet type, twist locking mechanism. Type C connections are a larger version of the BNC connection type, but much more durable and are used in applications up to ~11GHz. Note: Type C connections are also known as "big BNC".