Many people, by the way, are both. They have management jobs, but they realize that you cannot buy hearts, especially to follow them down a difficult path, and so act as leaders too.
Managers have subordinates
By definition, managers have subordinates - unless their title is honorary and given as a mark of seniority, in which case the title is a misnomer and their power over others is other than formal authority.
Authoritarian, transactional style
Managers have a position of authority vested in them by the company, and their subordinates work for them and largely do as they are told. Management style is transactional, in that the manager tells the subordinate what to do, and the subordinate does this not because they are a blind robot, but because they have been promised a reward (at minimum their salary) for doing so.
Managers are paid to get things done (they are subordinates too), often within tight constraints of time and money. They thus naturally pass on this work focus to their subordinates.
An interesting research finding about managers is that they tend to come from stable home backgrounds and led relatively normal and comfortable lives. This leads them to be relatively risk-averse and they will seek to avoid conflict where possible. In terms of people, they generally like to run a 'happy ship'.
Leaders have followers
Leaders do not have subordinates - at least not when they are leading. Many organizational leaders do have subordinates, but only because they are also managers. But when they want to lead, they have to give up formal authoritarian control, because to lead is to have...