Leaders may indeed vary the way they inspire people to change but this is when they have already decided on the need to change - hence leadership style does not reduce to decision making style. The idea of participative leadership is as silly as the idea of participative motivation. If a person has no desire to do an unfamiliar and difficult task, you may motivate him , by involving him in deciding how to go about the task at an early stage. Participative leadership is not possible because leadership involves one person persuading others to do something they would not otherwise do. The means of influence may be based in part on participation but this does not make leadership any less unidirectional .
Leadership is always unidirectional.
More than one person in a group may show leadership but each instance of leadership has to be to take the group in a slightly different direction or to make a difference in how the group is thinking. If one person simply echoes the original leader then that is followership. So, leadership may shift from one person to another in short order within a group, but each instance of leadership is unidirectional not participative. You have to occupy one position or the other at any one moment in time. Leadership is about advocating a change in direction, management is about executing that direction as efficiently as possible.