Ok I'll try, old topic but in case anyone does have the same question. Officially according to the DSM the only choices you have for the addict is Dependency and Abuse. Dependency is greatly if not totally inherited and Abuse is well, the best I can describe it is someone whom drugs/alcohol is causing a problem but they haven't had enough consequences to quit yet. (dependency rarely depends on consequences to quit, but more of a personally commitment) There are well defined symptoms of each. the word "Addiction" on the other hand is rarely used anymore other than AA or NA members. Dependency and Abuse are divided into categories of how long has it been since your use has caused you problems. as far as "abstaining addicts", it is a popular belief for AA and NA members to believe that they are addicts weather or not they are drinking/using (thus the inherited theory, which is fairly well supported by modern science now) Recovering addicts would would fall into the category of abstaining addicts however recovery usually indicates they have not "recovered" what they have lost yet but many use this term loosely even after they have recovered what they lost during their use. Abstaining addicts give no indication on weather they have recovered what they lost or not and often feel they will never be "recovered" and find it pointless to use the word recovering due to there being no realistic end to the recovery and just prefer the work abstaining to recovering. So the answer is purely semantic and a personal preference.
I haven't seen much about abstaining addicts, but you are right. An abstaining addict sounds like one in recovery.