Which is more accurate; change management lead to management change or management change lead to change management?

Change management purpose is to change people, and the ways they do things (processes, technology, and sometimes even their way of thinking) to achieve intended strategic objectives, as the organisation contains top management, middle management, and staff, changing the people top management will not necessarily lead to a successful change, but managing a change across the different layers will be more successful, and will lead to a change in the skills and decision making processes for managers.

I like the play with words but to be honest both statements are not accurate.
While a change in leadership can lead to a new direction and therefore could require the facilitation of change management.

Even though it is an unavoidable phenom, in general people are not well perceptive to change.
Developed organizations has well defined SOPs for its routine tasks.
So change in the management usually changes nothing or just a few nominal changes in the procedures or positions of resources.
Whereas in any developing or developed organization, when it comes to a major change in general operations/processes, organizational hierarchy, technology or HR practices; it requires change in perception, behavior, placement and utilization of materials as well as human resources.
Similarly the management philosophy and practice will also be changed.
So, in my point of view, both statements are correct but the first one is more valid.

be cool and patience to team member. Be aware from team member activities and put them on right path if they deviate

Both statements are not really accurate. Change management is the process of managing change or in other words it is essentially project management to implemement any sort of change within the organisation.

Management change is simply changes in people within management which may or may not lead to a major change within the organisation.

I think that "change management lead to management change" is more accurate.