An organization is a group based on membership with common goals, beliefs or practices.
Formal and Informal deal with the degree binding of membership, of commitment, oaths, control of authority or leadership, structure, facilities, fees, duties, and activities.
A third category would be on a more organic nature, or more as an organization based on interaction where each member is responsible for their own participation and actions. Operations and coordination are through lateral communication and mutual input and planning. Giving room for independent response or action to carry out main objectives or to maintain a current desire condition.
The latter is more of an organism than an organization. Organization function more on the control, leadership, and effort of the normal 20% (80%) ratio. The other functions on local pockets of members working together with no specified leader because it is driven by goals rather than orders.