Well I may have missed the point here–ALWAYS a distinct possibility–but it seems to me that this exchange started out with a question concerning the distinction (if any) between “communications” and { citizen engagement / customer service }. However it seems to have evolved into one regarding the distinction between those latter two terms. (An interesting communications “process” in and of itself!)

Postulating my understanding of the original question (!), my assessment of the discussion is that most participants seem to feel that {citizen engagement / customer service }–as a function–is not the same as the much broader concept of communications.

To the extent the more recent question regarding the difference between citizen engagement and customer service is not a semantical one, I suspect the answer lies most on whether the person receiving the engagement / service sees themselves at the particular time (or role) as a “citizen” or “customer” ….. That is, as D.D. writes, “the perspective of the people we are trying to reach.”