Management Skills != Leadership Skills
People management: concerned with the career growth, compensation, work satisfaction, etc of your reports. In a sense, this is a local extension of HR. Not a technical role. Must be well-versed in the issues related to employee effectiveness.
Project/Product/Program Management: concerned with planning, development, execution, and maintenance of products, services, etc. Should be technically competent but somewhat isolated from implementation.
Leadership: Inspires a team and fosters a culture optimized toward producing the desired result. Leadership skills are independent of other skills but complement them. Sometimes the action indicated by good leadership is contradicted by good management.
People managers deal in carrots, project managers deal in sticks, leaders deal in aspiration.