This seems to be one the long-standing arguments between people on the internet. When is something "irony" and when is it "sarcasm"? And can a quip be both at the same time?
Dictionary definitions don't seem to help much:
irony — the expression of one's meaning by using language that normally signifies the opposite, typically for humorous or emphatic effect
sarcasm — the use of irony to mock or convey contempt
In most of the arguments I hear about the words, neither of these definitions seem to match the definitions proposed by anyone.
Per Rhodri's request, I typically see definitions such as these offered instead of the ones I found in my dictionary:
sarcasm — using a sentence to convey its exact opposite meaning
irony — a circumstance that involves one's intent or actions backfiring and bringing about the opposite of what was intended, usually through humorous or coincidental means
Note that this just my construction. People have offered all sorts of other working definitions but the big difference is that "irony" involves a circumstance instead of an expression.