What's the Diff?

I have a BA in English so I'm supposed to know, but quite frankly, I don't really understand the difference between two words.  Every time I read both definitions I feel like I have it, then I don't.  See if you're as confused as I am:

 

sar·don·ic -

–adjective

characterized by bitter or scornful derision; mocking; cynical; sneering: a sardonic grin.

 

sar·cas·tic -

–adjective

1. of, pertaining to, or characterized by sarcasm: a sarcastic reply.

2. using or given to the use of sarcasm: to be sarcastic about ambition.

 

OK, that doesn't help much without having the definition of sarcasm.

 

sar·casm -

–noun

1. harsh or bitter derision or irony.

2. a sharply ironical taunt; sneering or cutting remark: a review full of sarcasms.

 

That's better.  So they both have bitter derision in their definitions.  But sarcasm may also be irony.  So does that mean that sometimes they mean the same thing?  The second definition of sarcasm states it may also be a taunt.  But sardonic can also be mocking.  So they do mean the same thing.  Right?