The 6SK7 is a variable μ pentode for RF and IF amplifiers in superhet receivers. The gain of the device being controlled by a negative voltage derived from rectifying the final IF signal. In this way strong signals do not overload the receive chain because the various controlled stages have their gain reduced.
The American Type designations such as 6SK7 refer to a single ended version of another Valve in this case the 6K7.
The 12SK7 had identical characteristics apart from the heater. The 12.6 Volt heater being used directly across a vehicle battery.