westfw:
I was under the impression that flash memory was another type of EEPROM
Yes, and no. The 32k of "flash program memory" in an ATmega328 is not usable for writing data, and has a limited number of cycles when being written by anything.
Technically both the Flash and the EEPROM have a limited amount of write/erase cycles, though in the AVR chips used in Arduinos there is at least an order of magnitude difference (i.e. a factor of ten) in the minimum times a memory space can be rewritten in EEPROM. For example in Section 7, "AVR Memories", of the ATmega328 datasheet it states; "The Flash memory has an endurance of at least 10,000 write/erase cycles" and "The EEPROM has an endurance of at least 100,000 write/erase cycles".