I prefer "natural language processing" over "computational linguistics" because NLP/CL has very little to do with the goals of linguistics. Like you mentioned, linguists are after the truth of what actually happens in the mind to make language work. NLP folks are after what works -- any answer will do.
Being practical is fine, of course, but it just irks when NLP is billed as a science that is trying to "discover" something deep and real about the world. You often see young NLP students who take linguistics courses wanting to bring over some of the (cognitive) stuff they learned in these courses over to NLP. This is well-intentioned, but naive. NLP is an engineering discipline and, as such, the answer that provides the best results is the best one regardless of what it's cognitive viability is.
Being practical is fine, of course, but it just irks when NLP is billed as a science that is trying to "discover" something deep and real about the world. You often see young NLP students who take linguistics courses wanting to bring over some of the (cognitive) stuff they learned in these courses over to NLP. This is well-intentioned, but naive. NLP is an engineering discipline and, as such, the answer that provides the best results is the best one regardless of what it's cognitive viability is.