The general term for such counsel would be "business lawyers". Writing contracts is one of their many duties and where they recognize the hazards and potential vagaries at the periphery of their expertise, they may opt to join a better-qualified co-counsel to assist.
For instance, contracts for hiring free-lance writers or photographers may involve complicated legal analysis of copyright ownership, better addressed by seasoned intellectual property counsel.
Even as a former corporate attorney, I would likely retain personal counsel to at least review, if not draft, any important contract involving myself. That way, were anything to "go wrong" in the execution, there would (in theory) be another attorney responsible for it.