EEPROM (Electrically eraseable programmable read only memory) is the generic acronym for a whole range of persistent but electrically eraseable memory technologies. Flash is just one of those EEPROM technologies.
Some types of EEPROM are byte reprogrammable and this type is commonly used to provide a small area of alterable memory like in some microcontrollers and some people reserve the name EEPROM for this but that is strictly incorrect. Flash is a technology where erasing is done in blocks which normally allows higher density and faster speed.