Full-Text Search in PostgreSQL: A Gentle Introduction
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2.1. FTS operator

TSQUERY @@ TSVECTOR TSVECTOR @@ TSQUERY

Returns TRUE if TSQUERY contained in TSVECTOR and FALSE otherwise.

=# select 'cat & rat':: tsquery @@ 'a fat cat sat on a mat and ate a fat rat'::tsvector;
 ?column?
 ----------
  t
=# select 'fat & cow':: tsquery @@ 'a fat cat sat on a mat and ate a fat rat'::tsvector;
 ?column?
 ----------
  f

TEXT @@ TSQUERY VARCHAR @@ TSQUERY

Returns TRUE if TSQUERY contained in TEXT/VARCHAR and FALSE otherwise.

=# select 'a fat cat sat on a mat and ate a fat rat'::text @@ 'cat & rat':: tsquery;
 ?column?
----------
 t
=# select 'a fat cat sat on a mat and ate a fat rat'::text @@ 'cat & cow':: tsquery;
 ?column?
----------
 f

TEXT @@ TEXT VARCHAR @@ TEXT

Returns TRUE if TEXT contained in TEXT/VARCHAR and FALSE otherwise.

postgres=# select 'a fat cat sat on a mat and ate a fat rat' @@ 'cat rat';
 ?column?
----------
 t
postgres=# select 'a fat cat sat on a mat and ate a fat rat' @@ 'cat cow';
 ?column?
----------
 f

For index support of FTS operator consult Section 2.7.