Computers have a few types of memory; temporary (short-term) or permanent (long-term). RAM is a type of short term memory, or where computers remember stuff that it is working on at that moment; but if the computer loses power, it forgets everything in short-term memory. So to help with that, we have permanent storage (memory). Long term memory (or permanent memory) is for things that we want to remember for long periods of time or even if you lose power. In computers, we often do this by "saving" (writing) chunks of memory (files, pages or programs) to some device that is meant to provide our permanent storage. Later we can "READ" (get or open) those files/programs from this long-term memory. In mobile devices it's usually saving constantly, to hide the saving files from the user.
Now there's a type of chips based memories that are "permanent". One type allowed people to just "stamp out" the chips (in manufacturing) with all the information permanently on it. You could never change it (write to it), so it was called "Read-Only Memory" or ROM. This is used for the few things that the computer must know in order to start up, or on some computers for a few "built-in" functions or files, but most people want their computers to save their files or to add their own programs.
With that in mind, we invented special types of ROM that you could "change". Sometimes you need to write the data to the chip once; that is called PROM - Programmable Read-Only Memory. If you need to change the data, you throw away that chip, and replace it with a fresh one. Since that wasn't practical for many things, we invented ways to erase the data. Some chips required Ultra-Violet Light to erase, called EPROM - Erasable Programmable ROM. Later, we figured out ways to make chips that could be erased electrically or EEPROM (Electricly Erasable PROM). Or there's another type of the same thing called NV-RAM (Non-Volatile, meaning permanent). But programmable and erasable permanent storage chips are still far more expensive than regular memory chips, so they are used for a few things like memory in your PDA's, digital cameras or your cell-phones. But for lots of permanent computer storage, we created specialized devices.
There are many devices for long term storage. The most common one is a hard-disk drive. A hard-drive has many small rigid magnetic platters stacked on-top each other (with some space between them) and spinning very quickly, with a little arm that can move in and out, and access any of the "tracks" (magnetic channels) on those disks.
Hard-drives are not the only types of long term storage. Floppy Disks are another kind, so named because the disk itself is much thinner and is on a plastic material that is flexible (floppy). Early ones were in flexible paper shells, later ones came in hard plastic shells; so were no longer "floppy", thus confusing people forever.
Other forms of permanent storage include CD's or CD-ROM's (Compact Discs). Or DVD's or DVD-ROM's (Digital Versatile Discs). These are little "optical" discs, with very small pits printed/stamped on them. We can stamp music or movies on them for your entertainment system, or for computer, just stamp lots of data (programs or files). Hence why they're called "CD-ROM" or "DVD-ROM", they are "Read-Only".
Some types of CD's and DVD's allow you to program them once; but instead of just calling them CD-PROM's, they sometimes use new terms; like CD-R (Recordable) or WORM (Write-Once Recordable Media) but it is the same idea as PROM. And later, we have rewritable versions of CD's or DVD's, which are called CD-RW (Read/Write) or DVD-RAM.
Most of these have been displaced by NV-RAM, or Non-Volatile Memory: also called thumb drives, memory sticks, or SAN disk (which is a brand, not a type of memory).
Now you should be a guru of computer memory types, and know a lot more about these terms and what these different things do.