Short answer
Managing is about bringing order to complex work: planning, organizing, staffing and checking results. Leading is about helping people through change: setting direction, getting people aligned behind it and motivating them. John Kotter drew this line in Harvard Business Review in 1990. In practice, anyone who runs a team needs to do both. Most new managers are trained, if at all, on managing. Leading is the part they’re left to figure out.
The longer answer
The distinction isn’t about rank. A frontline supervisor can lead, and a senior executive can spend all day managing.
Where it matters most is the step from individual contributor to manager. People are promoted for being good at the work. Their first job is to manage it. But the problems that slow companies down, like turf fights, stalled initiatives and decisions nobody owns, need leading.
Good development teaches both, in that order: get the basics of managing right, then build the skills of leading across the team and beyond it.
Sources
John P. Kotter, “What Leaders Really Do,” Harvard Business Review, May–June 1990