An autocratic approach relies upon formal power and/or physical strength - the goal is to ‘require’ the adoption of ‘orders’ from the top. It is often used in time-critical situations where operational procedure, defined by the leader, needs to be adhered to for success.
A democratic approach relies upon consensus being formed by a group such that the majority of parties agree to the solution. It is often used in non-time-critical situations where buy-in to the solution by multiple stakeholders is advantageous.
A laissez-faire approach approach relies upon the leader being ready and willing to accept the skill and expertise of their subordinates’ solutions and actions. It is often used where are easily measured and the procedure for achieving the outcome is not important.