In addition to the solution with 'aaaaaaaa' LIKE '%' || tag_name || '%'
there
are position
(reversed order of args) and strpos
.
SELECT id FROM TAG_TABLE WHERE strpos('aaaaaaaa', tag_name) > 0
Besides what is more efficient (LIKE looks less efficient, but an index might change things), there is a very minor issue with LIKE: tag_name of course should not contain %
and especially _
(single char wildcard), to give no false positives.