ROM = <b>R</b>ead-<b>O</b>nly <b>M</b>emory
PROM = <b>P</b>rogrammable <b>ROM</b>
EPROM = <b>E</b>rasable <b>PROM</b>
EEPROM = <b>E</b>lectrically-<b>E</b>rasable <b>PROM</b>

Yes, the terms are getting more specific as you go down.

"EPROM" is usually taken to mean "UV-EPROM" unless otherwise specified; <i>ie,</i> the <b>E</b>rasing is done by exposeure to <b>U</b>ltra-<b>V</b>iolet light

Sometimes, UV-EPROM chips are packaged without the little window to allow the UV light in (which is much cheaper); thus, in practice, it is not possible to actually erase these chips once they've been programmed.
Hence they are known as "<b>O</b>ne-<b>T</b>ime <b>P</b>rogrammable" or OTP.

Yes, <b>Flash</b> is a particular Electrical-Erasure technology (developed by Intel, I think).
I think they called it "Flash" to indicate that it can be erased "in a Flash"