There are actually more than two kinds of DVD discs.
The best thing I can do is refer you to an excellent article that
explains them all, then I'll give you a summary. Here's the article:
Don't Be Stumped By DVD Standards
To summarize, there are basically two general kinds of DVD discs for
recording. One type allows you to record only once, while the other
type allows you to record over and over again. Drives and discs for
record-once DVDs cost less than the rerecordable kinds, as you'd
expect. There's no real difference in quality, but the reusable kind
is obviously much more convenient to use for most purposes.
One of the problems is that there are some differences in recording
standards, so a DVD you wrote on one drive might not necessarily work
in another drive. If you're only using one computer, there's no
problem. But if you're using two computers, you should make sure they
have compatible drives. The difference is kind of like that between
VHS and Beta videotapes back a decade or so (or maybe it was longer).
They both work well, but they're not compatible with each other. Your
choice in picking DVD-RW or DVD+RW is a matter of personal preference
and which manufacturer you prefer; I have found no indication that one
is markedly superior to the other.
Here, then, are the types of DVD discs:
DVD-R(A) record once
DVD-R(G) record once
DVD+R record once
All of them should play in modern DVD players hooked up to your TV.
If you go past the middle of the page referenced above, there's a
chart that what type of disc is compatible with which hardware. If
you're buying discs, you need to buy the type that goes with the kind
of drive you have.
There are also rewritable DVD-RAM discs that are used for data storage
rather than video, but they don't play in DVD players. The ones made
for video can also be used for data storage (such as to back up a hard
Here is a more technical article explaining the different types of
DVDs and their compatibility:
DVD Standards Comparison by Drive Generation
I hope this fully answers your question.
Google search terms used:
"types of DVDs"