If I were to answer for me, my opinion, I would have to say they are synonymous.
However, if I were to answer according to AA/NA (the organisations, not the opinions of their members), I would have to say that 'clean' is an NA term used to mean free from all mind altering drugs (with the exception of nicotine and caffeine), and that 'sober'/'sobriety' are AA terms defined as freedom from alciohol (see AA's Singleness of Purpose and the pamphlet Problems Other Than Alcohol).