As others have stated...
ROM : Can not be programmed. Created as-is from factory
PROM = Can only be programmed ONCE. Once programmed they can not be changed.
They are usually smaller (in size and memory space) than eproms, but faster
EPROM = ERASABLE PROM . Can be re-used if you erase them by shining a UV light
through a small glass window in top of the chip.
E-EPROM = Same as EPROM, but can be erased by electrical voltage.
(ie. this means you can re-program them without needing a UV lamp )
For Williams games, most eproms are 2732 chips.
The sound boards however user 2532 eproms.
Just about every programmer will do those eproms.
However, if you want to do proms, you'll need a more specialized programmer,
...and usually an older model (circa 1980-1985)
The Data I/O 29B will do just about any chip from the 80's,
but it's a temperamental beast and hard to find a reliable working one.
(...I've had 4 before finding one that worked well )
Good luck.
Steph