From
www.reference.com:
The psychological state of sympathy is closely linked with that of empathy, but is not identical to it. Empathy refers to the ability to perceive and directly experientially feel another person's emotions as they feel them, but makes no statement as to how they are viewed. Sympathy, by contrast, implies a degree of equal feeling, that is, the sympathiser views the matter similarly to how the person themselves does. It thus implies concern, or care or a wish to alleviate negative feelings others are experiencing.
Thus it is possible to be:
Empathic but not sympathetic, by internally experiencing another's feeling but not being motivated to alleviating action as a result (eg, a lust killer who is aroused by his victim's fear, or a con artist who knows how his mark feels but uses it to manipulate not support).
Sympathetic but not empathic by realising (perhaps cognitively) someone is upset and wanting to alleviate that, but not experiencing their sense of upset directly and internally as an emotional state within themselves (eg, a person at a help desk who sees another in distress, does not feel distress themselves, but tries to find what is wrong and help them anyway).
In short:
Sympathy: I imagine your pain and wish I could help.
Empathy: I feel your pain; I know your pain.
I have more commonly heard people use sympathy in all cases as I don't think a lot of people really know the true meaning of empathy, so they therefore misuse sympathy (and most likely misuse empathy when they try to use it).