Again, these terms are not universally defined. OD consultants often work with managers (and others), so they function as management consultants. Their work often results in improved management systems and methods, as well as other changes.
But there are many management consultants, business consultants, and others, whose orientation and methods are very different from ones used in OD. They use a "doctor-patient" approach, in which the client tells them what the problem is, and the consultant performs some kind of analysis, delivers recommendations, and leaves.
OD uses a Process Consulting approach in which we join with members of the client organization to define the goals of the work, and then we guide a participative sequence, including joint data-gathering, problem-solving, action-planning, implementation, and assessment of the project. "We don't just feed the hungry--we also teach people how to grow their own food."