I just asked my pastor that same question. They are all synonyms. Take a look at how they are used in Psalm 51:1-5, 9, 13, among other places.
I agree, and I think emphasizing something by using synonyms in triplicate is not uncommon in Scripture:
Exo 34:7 '...iniquity and transgression and sin...'
Deu 5:31 '...commandments and statutes and judgments...'
Mat 22:37 '...with all your heart, with all your soul, and with all your mind...'
Act 2:22 '...miracles and wonders and signs...'
Eph 5:19 '...psalms and hymns and spiritual songs...'