for example :
the records "a substring b" and "substring c d" would be a match, and so would "xxx" "aa xxx" etc. If possible: I'd like returned the substring, or the indexes of it's beginning and end in one of the strings.

SELECT  t0.s FROM  t t0 , t t1 WHERE  position(t0.s IN t1.s) <>0 GROUP BY t0.s HAVING count(*) > 1
A quick answer based on the idea that you join a table with itself to produce a t^2 from which you select only those who have something in common. The grouping and the having clause are used to filter out rows produced by a row with itself.

My previous answer
SELECT  t0.s FROM  t t0 , t t1 WHERE  position(t0.s IN t1.s) <>0 GROUP BY t0.s HAVING count(*) > 1
obviously does not fullfill the requirements.

use the "like" comand
SELECT string FROM TABLE WHERE string LIKE '%' + @substringTocompare + '%'


where the special character '%' is a comodin for find all substring similary.