An excellent question! Certainly there is a lot of overlap here. Succession planning without career planning can be invalid (i.e. we are deciding potential career paths for employees without their input - no employee wants that!). Career planning without succession planning can be ineffective (employees are working on developing competencies for potential career paths, but the company has no internal succession discussions or processes in place to help make these potential career moves happen).
So Succession Planning pertains to the organizational strategy, processes, discussions, tools and structure to help identify where employees could potentially move in their career inside the organization, and the development actions needed to help build knowledge and competencies and qualifications to support potential career moves for employees inside of the company.
And career planning pertains to the individual planning, discussions, tools and development actions an employee can take, working with their manager, and working with HR and other business leaders in the company, to identify potential career paths and to take actions to prepare for future potential career options.
So married together, succession planning strategy and tools, and career planning strategy and tools, provide a more complete structure in an organization for successful internal talent retention, development and career movement, resulting in lower external recruiting costs for the company and in enhanced career possibilities for employees - a win-win for everyone!