Basically, sardonic and sarcastic both stand for mocking gestures, but what is the difference in their contextual use?
Are there any other words that represent a similar gesture?
@Manoochehr doesn't quite catch the meaning of sardonic. It means "grimly mocking or cynical." My Webster's gives its origin as
mid 17th cent.: from French sardonique, earlier sardonien, via Latin from Greek sardonios ‘of Sardinia,’ alteration of sardanios, used by Homer to describe bitter or scornful laughter.
It really doesn't carry the connotation of superiority or low opinion all by itself, although such feelings may accompany it.
Sardonic is in fact distinct from sarcastic but not by much, and many people use the two as if they are interchangeable, which, strictly speaking, they are not. Sardonic is more extreme and negative, and one can be sarcastic without being sardonic, and vice-versa.
Sarcastic: Well, this meeting with the boss should be hilarious.
Sardonic: Time for the monthly flogging by a twerp in a suit; I'll try not to get blood on the executive carpet.
Sardonic humour is mocking, but not necessarily sarcastic; sarcasm is stating a counterfactual, whereas sardony is a moment of grim poetic humour and may or may not contain counterfactuals. The above example uses melodrama rather than sarcasm as a device.
According to Longman Dictionary of contemporary English:
He looked at her with sardonic amusement.
Was she being sarcastic?
He can’t help making sarcastic comments.
sarcastic manner/smile/laugh etc
‘I thought so,’ she said with a sarcastic smile.
The definition of the words I can read on the NOAD are:
She wrote sarcastic comments on their failures.
She's witty and sarcastic.
Starkey attempted a sardonic smile.
The differences between the words are:
The NOAD, in a note titled The right word, reports also:
Irony is the implicit humor in the contradiction between what is meant and what is expressed, or in the discrepancy between appearance and reality. An example would be to shout, in the midst of a hurricane, What a perfect day for a wedding!
Although sarcasm may take the form of irony, it is less subtle and is often used harshly or bitterly to wound or ridicule someone. Unlike irony, however, sarcasm depends on tone of voice for its effect ("a fine friend you turned out to be!", he said, with obvious sarcasm).
To answer the currently unanswered half of the question:
Criticism, if done correctly, is different to sardonism or sarcasm in that they are a mode of voice, while criticism should be a balanced review of a subject. Unfortunately, bad criticism generally comes over as sardonic and sarcastic - so, you can see the confusion.