What is the difference between a MEL, MMEL, KOEL and Equipment List?
Definition of Master Minimum Equipment List from ICAO Master Minimum Equipment List/ Minimum Equipment List Policy and Procedures Manual:

“Master Minimum Equipment List” means a document approved by the Director General that establishes the aircraft equipment allowed to be inoperative  under conditions specified therein for a specific type of aircraft.
A Master Minimum Equipment List (MMEL) is an approved document created specifically to regulate the dispatch of an aircraft type with inoperative equipment. It establishes the aircraft equipment allowed to be inoperative under certain conditions for a specific type of aircraft and still provide an acceptable level of safety. The MMEL contains the conditions, limitations and procedures required for operating the aircraft with these items inoperative. The MMEL forms the basis for development and review of an individual operator's  Minimum equipment List (MEL).

Definition of Minimum Equipment List from the same document:

“Minimum Equipment List” means a document approved by the Director  General that authorizes an operator to dispatch an aircraft with aircraft  equipment inoperative under the conditions specified therein.

and

The MEL is a joint operations and maintenance document prepared for or by  an operator to:
a) identify  the minimum equipment and conditions for an aircraft to maintain the Certificate of Airworthiness in force and to meet the operating rules for the type of operation;
b) define operational procedures necessary to maintain the required level of safety and to deal with inoperative equipment; and
c) define maintenance procedures necessary to maintain the required level of safety and procedures necessary to secure any inoperative equipment.

Regulatory authorities use similar definitions. For example, Transport Canada uses nearly the same definition, replacing 'Director General' with 'minister'. So the ICAO definition can be used as the base.
Kinds of Operation Equipment List (KOEL) are lists one finds in some aircraft POH that indicates what equipment (generally optional) si required for flight under certain conditions. From FAA Advisory Circular Minimum Equipment Requirements for General Aviation Operations under FAR PART 91 AC NO: 91-67:

Kinds of Operations List (KOL). The KOL specifies the kinds of operations (e.g., visual flight rules (VFR), instrument flight rules (IFR), day, or night) in which the aircraft can be operated. The KOL also indicates the installed equipment that may affect any operating limitation. Although the certification rules require this information, there is no standard format; consequently, the manufacturer may furnish it in various ways.