I think the issue here is the fact that in the U.S., lawyer attorney at law and counselor at law are the same thing... in other countries they are not necessarily the same person.
Most intuitively think of a lawyer as an Attorney where he or she is hired to as a representative in court or with others.
However, lawyers also acts as counselors. Sometimes counselors are trial lawyers but they can also just be giving legal advice.
Hannity could be telling the truth.
Cohen never acted as his representative but he may have given him advice.