The interest of urban planning is at the city level and focuses on functional relations, While urban design deals with part of the city (specific location), it cares about aesthetic and functional aspects
Urban design is broader than urban planning, also incorporates architecture, landscape architecture, even civil and traffic engineering. It uses an interdisciplinary approach to make urban areas functional and livable.
I agree with your idea about the Urban design incorporates architecture, landscape architecture, even civil and traffic engineering. but on the other hand, I think like many other Architects and urban planners that Urban planning is broader than Urban design, not the opposite as you confirmed.
Urban planning often addresses big issues that related to policy, regulations, standards, and codes. It is more about long term-value. Urban design deals with features and details put in limited scales. It is more about place-making and forming spatial and physical features.
Urban Planning focuses on City planning, regional planning; actually it is kind of broader topic than Urban design. Because Urban design is taking about small scale dedesigning in urban areas. But urban planning means larger scale topic.
I am agree with @ Thakshala kumari. According to my point of view, Designing is the part of the planning. It is not vast concept. Otherwise, planning can be considered as science. Designing may be supported to art.