PROXIMITY (or NEAR) gets results for terms which appear in close proximity to one another within the resulting page hit. The specific required distance for this operator is generally down to search engine defaults.
NOT NEAR (or FAR) is an operator that requires the search terms not be within a default number of words’ distance.
FOLLOWED BY or NOT FOLLOWED BY are operators that return or exclude results for pages where one term directly follows the other one.
SENTENCE is an operator that requires the searched terms be within the same sentence.
W(#) is a search operator that gets results for pages with terms which are within a number of words distance as specified with a numeral following the operator, such as W(5) for example.
AROUND(#) is an unsupported Google operator that indicates how many words can separate the searched terms, similarly to W(#).