There is no difference in law between an Executive Director and a Non Executive director.

The appointment process is exactly the same.

How do I appoint an individual as a director?

An executive director is a member of the board of directors and an employee of the company. He/she will have a specific role such as finance director and as such be responsible for the day to day running 
of the company within this sphere.

A non executive director is a member of the board who is not an employee but appointed for his/her expertise and takes a part in decision-making at board meetings. Sometimes non-executive directors may get involved in such things as disciplinary hearings, especially for high ranking 
employees.