A business owner asked me recently whether he should focus on improving leadership or management first. In my workshops, we define leadership development as helping people increase their self-awareness, think critically and behave kindly so they can inspire others to succeed and generate positive results for the organization. Management is one facet of leadership that addresses specific work-related tasks including managing people and processes.
Whether you call it leadership or management, it all comes down to how people in positions of power behave toward their co-workers and employees and the kind of results they generate. Once you build leaders who are happy and healthy, you won't have to worry about whether they're leading or managing because they'll do both effortlessly. The idea is to encourage people to learn core skills that help them feel great about themselves, treat others well and get things done.
The difference between leadership and management is that true leaders manage everything with grace and managers tend to get stuck in the details. Focus on building an environment that encourages people to be inspiring leaders and you won't have to worry about who does what.