It developed thus:

PROM: programmable read only memory.
Someone discovered that you could erase it with UV light so they started leaving a clear window in the top (quartz) so we get:
UV EPROM: Ultra violet erasable programmable read only memory. Usually just called EPROM.
Time passes and they developed a way of storing the information permanently but making the chip able to be erased electrically, to distinguish it from a UV EPROM it became known as:
EEPROM: As above.

It is quite common now to leave off the first E as UV EPROMs are rarely used other than in historical equipment.

EEPROM is often also written at E^2PROM or E2PROM or E squared PROM.

You also get MPROM which means mask programmed. That is used for commercial production runs where the manufacturer will programme at manufacture with a fixed data set, non modifiable and non erasable.

There are other obscure things but life's too short.