In the U.S. vocabulary the word relish refers to condiment which normally contains vinegar, salt and sugar. The condiment might also contain chopped fruits or vegetables such as a "pickle relish". The word "relish" first appeared in English in 1798 and comes from the word "reles" which means in Old French, "something remaining".
To the British the term relish refers to a thick pickle or sauce which includes vinegar.
Relishes probably came about out of a desire to preserve vegetables from the home garden for use during the winter months when no fresh produce was available.
The piccalilli and chow-chow images are from Blyers Relish House. These traditional hand made relishes are available online at Blyers Relish House.