Cheating --- Any behaviour that a player uses to gain an advantage over his peer players or achieve a target in an online game is cheating if, according to the game rules or at the discretion of the game operator (i.e. the game service provider, who is not necessarily the developer of the game), the advantage or the target is one that he is not supposed to have achieved.
Exploit: To make full use of and derive benefit from a resource. Often used in a negative connotation in which the individual is deriving an unintended benefit from the improper use of a resource.
Common Forms of Cheating 
Cheating by Exploiting Misplaced Trust
Too much trust is placed on the player side, which in reality cannot be trusted at all because the cheating player has total control over the game. This form of cheating can be seen by a single individual who has been asked to police himself in a game i.e. a player is asked to buy five sandwiches in order to get the sixth for free, if his purchasing habits are not monitored in some way the player can exploit the misplaced trust and claim to have made the needed purchases when he has, in fact, not. This form of cheating can be seen between multiple players when one player, the con-man, gains the trust of another player, the mark, and uses that trust to achieve a goal i.e. in a game where a player is required to turn in 100 tokens, a con-man may convince a mark to give him 50 tokens now for the promise of more tokens later. The con-man then turns in 100 tokens for the prize and never repays the mark.
Cheating by Collusion
Players may conspire with one another in order to gain an unfair advantage within a game. If, for example, a game requires a player to get 10 "wins", a player may agree to purposefully lose should the winning player agree lose on their next match.
Cheating by Abusing Game Procedure
A player exploits an aspect of the game in order to create a personal advantage. An example is when a player has one try to solve an online puzzle in 30 seconds, if the players believes he will not complete the task, he may disconnect from the internet before the timer runs out, effectively giving him another chance.
Cheating Related to Virtual Assets
If a player offers to exchange actual goods for virtual goods, the player may cheat by not fulfilling their end of the bargain.
Cheating by Exploiting Machine Intelligence
The use of artificial intelligence constitutes a common form of cheating in puzzle or logic based games. An example of such cheating would be the use of a program designed to create words from random letters for a game of Scrabble.
Cheating by Modifying Infrastructure
Without modifying the game itself, a player can cheat by modifying the infrastructural of the tools used by the game. If a player is asked to click a link once every 24 hours, he may be able to set his computers time ahead by one day, allowing him multiple visits in a single sitting.
Cheating by Denying Service to Peer Players
A player may actively pursue keeping others from joining a game, or forcing others to leave a game, in order to improve his chances of success. A simple example would be for one player to tell another an incorrect start time for a game, making the duped player miss the competition.
A player who has completed his requisite task may hold off from submission until another player submits, the first player would then alter his entry based on the entry of the first.
Cheating by Compromising Passwords
A player gains access to the data of another player by means of procuring that players password.
Cheating by Exploiting Lack of Secrecy
If a player comes in to possession of secret information from another player, the first player may exploit this information to his advantage.
Cheating by Exploiting Lack of Authentication
A cheater may pose as a game official in order to gain access to private information.
Cheating by Exploiting a Bug or Loophole
Neither compromising the game nor the tools to play the game, the player exploits a loophole for personal gain. If a game requires a player to make 50 qualified calls, but the game only checks to see whether the player made a call, a cheater may exploit the loophole and simply make unqualified calls.
Cheating Related to Internal Misuse
A game operator who has administrative access uses that access to advance in the game.
Cheating by Social Engineering
Cheater trick a player in to believing something bad has happened to their game and ask for the players password to make it right.