Precisely:

ROM = Read-Only Memory - not user programmable;
PROM = Programmable Read-Only Memory - not user erasable;
EPROM = Erasable Programmable Read-Only Memory.

EPROM comes in UV-erasable and Flash-erasable varieties; Flash EPROM is often just called "Flash" for short.

Of course, from a code-execution viewpoint, the ROM/PROM/EPROM distinction is completely & totally irrelevant