Thermal Efficiency only takes into account (essentially) how effectively you're burning fuel or turning fuel into heat. The Energy Factor then also takes into account things such as standby heat losses in a tank. So a tank may sometimes burn fuel efficiently but then lose some of that heat at standby. The Energy Factor is always going to be equal to or less than the efficiency.
The term ‘Energy Factor’ characterizes the efficiency of both tank and tankless water heaters. The Energy Factor is the portion of the energy going into the water heater that gets turned into usable hot water under average conditions. It takes into account heat loss through the walls of the tank, up the flue, and in combustion. The higher the Energy Factor, the more efficient the heater.
Because tankless water heaters don’t have the losses associated with tanks, their Energy Factors are normally higher (although well-insulated, ultra-efficient tank heaters also have high Energy Factors). Energy Factors for gas tankless water heaters range from around 0.69 to 0.84, compared with 0.55 for a conventional tank and 0.86 for an ultra-efficient tank heaters.
Conventional electric tank water heaters have an Energy Factor of about 0.87 compared with 0.91 for an ultra-efficient tank and 0.98 for electric tankless heaters.