Flash is also a type of EEPROM.
One of the problems with all of this is that some of the terms themselves are not really logical, and different technologies with some different attributes have been 'bundled in' with existing acronyms. For instance, an old-fashioned EPROM is just as random access as static RAM, at least for writing, so could just as easily be called RAM. However, the term 'RAM' implies that the memory can be changed without resorting to bulk erasure.
The term EEPROM tends to be used for memory which is byte-erasable, as opposed to flash which is arranged to be b-erasable. Both can be considered random-access because locations can be individually addressed and read pretty much immediately, unlike a tape which is sequential access (so is a hard disk - but that is fast enough to also be called 'random access').
I'm a relatively old git now, so I've seen the changes in use of terms as new memory types are grouped in with older ones.