Definition time. I’ll go for normative ones, even if they can be argued against.
I assume that rules are used, where rules are the perceived and accepted procedures of play. This includes such sentiments as “follow GM plot hooks”, “roll d20 and add skill, higher is better”, “all players can create facts about their own character’s homeland as long as GM okays the facts, which usually happens”. (For those who know system in Forge theory: This definition of rules has significant overlap with system in the Forge sense, but is not equivalent, and neither is a subset of the other.)
Resolution is using rules to determine diegetic (fictional) facts. This particularly means that there exists at least two different outcomes of the resolution such that they must have different implications as far as the fiction is considered. For example: Rolling attributes in D&D. Different results lead to different diegetic outcomes. A trivial example is GM narration, but it is also not very relevant to this blog post. I’ll talk about the non-trivial cases, in which some other factor is used to restrict narration or the fiction in general. Random encounters are a good example.
Disclaimer: I don’t like fudging.
A participant (player or GM) fudges when resolution rules are used and their effect wrt the diegesis is ignored. Note: Player fudging is usually cheating, which I define a bit later.
For example: Player rolls a lousy set of attributes and rolls a new one and displaces the worst with it. It is worth noting that this is only fudging if it is not assumed in the group. GM rolls a random encounter, which is zombies, again, and uses skeletons instead. This, again, is fudging only if GM usually uses the encounter tables as is, with no need to alter the results afterwards. By this definition, it is not fudging to alter the mechanical statistics of entities mid-game, which might mean this is a bad definition. I’m not sure.
Participant is cheating when some rules are used or are not used and the group does not approve of this, or would not approve if it knew.
Particularly: Game masters who fudge or alter statistics of NPCs or spontaneously swap the place of cities are cheating if and only if the players do not or would not accept it. If, on the other hand, the players assume or would accept such activity, it is not cheating (but may still be fudging). Almost all player fudging is cheating. In some games, GM fudging is also cheating. In others, not so much, but this still is a matter of the group.
Fudging is not inherently bad. Cheating often is. Not all fudging is cheating. Not all cheating is fudging (player reducing too few hit points is, but adding them during a calm moment is not).
Also, my definition of fudging doesn’t seem to work properly. It needs a bit more refinement, I think.