Question: In the field of Data Mining, is there a specific sub-discipline called 'Similarity'? If yes, what does it deal with. Any examples, links, references will be helpful.

Also, being new to the field, I would like the community opinion on how closely related Data Mining and Artificial Intelligence are. Are they synonyms, is one the subset of the other?

Thanks in advance for sharing your knowledge.

Answer: 
Appropriate definitions of 'similarity' (which features you extract, what you do with them afterwards) are almost the definition of clustering, and clustering is a fairly wide sub-field of data mining.

If you make the standard cynical definition of AI as the set of problems we can't solve well (indeed, that we can't specify well enough to start solving), data mining shades into it once the space in which you're looking for correlations starts to be larger than your algorithms can handle.
There are lots of similarity measurement used in data mining. for text mining, to find similarity in texts, cosine similarity, jaccard similarity widely used

For reference, you can see raghavan and amnnings information retrieval book