From Dictionary.com:

sar·casm    ( P )  Pronunciation Key  (särkzm)
n.

1. A cutting, often ironic remark intended to wound.
2. A form of wit that is marked by the use of sarcastic language and is intended to make its victim the butt of contempt or ridicule.
3. The use of sarcasm. See Synonyms at wit¹.

And here's the definition of passive-aggressive:

http://www.ces.purdue.edu/anr/field/gob/forms/passiveaggressive.html

Passive-Aggressive People

Passive-aggressive people avoid direct response, but "get even" with other people later for real or imagined slights.

This behavior is interesting because it's a hybrid of two other styles. Passive people behave passive-aggressively when they become "fed up." Aggressive people behave passive-aggressively when they perceive that they can't act in their normal aggressive fashion (usually because of an authority situation). For instance, an aggressive person who works for an aggressive boss will not tackle the boss directly, but will get even later.

It's often hard to tell when a person will behave passive-aggressively because passive-aggressive people collect a full "green stamp book" before they blow up. Because they don't tell others when something bothers them, they give permission to continue behavior which offends them. After they have a full green stamp book (in other words, when they decide they're fed up), they blow up.

Passive-Aggressive Behavior Clues