Inno uses the terms "fighter" and "farmer" as options on play style. Used to be there were clear roles for players to choose one or the other. Back when GvG was the main auxiliary (meaning not in the main city) feature, guilds would have players who were active fighters and others who concentrated on producing and donating goods and/or units for defense armies. Since there were fewer and less intense events, either choice was feasible.
Then events intensified, and other game features came along. In addition to this, power creep in many forms entered the game, accelerating with each passing event. Military boosts grew and grew. Event buildings started replacing coin, supply and goods buildings in producing resources, along with starting to provide significant military boosts. Once Future Era arrived, there were now three GBs producing guild Treasury goods. No longer was it necessary for guilds to have dedicated farmers. Anyone could fight while also providing resource support for the guild through those GBs.
The final death knell for farming in Inno's sense of the word was the introduction of GBG, with it's rather significant rewards and seemingly unlimited fighting. Between rewards from fighting in GBG and resources provided by event buildings and GBs, you could set up your city for maximum fighting capability and not lose anything on resource production.
Farming from the players' perspective originally referred to battle point farming in GvG. Back when global ranking meant something to a majority of players. Later it started to refer more to auxiliary worlds set up to "farm" Diamonds, first from Wishing Wells and then later from participating in GE with its Diamond rewards. Apparently some people refer to this as "mining", but I've never heard that term much or used it at all in this sense. When GBG came along, farming took on a new meaning, now mostly referring to heavy GBG participation resulting in considerable resource rewards, from goods to Diamonds.
So now to today. Farming can still mean either having one or more Diamond farms, or heavy GBG participation. Fighting really doesn't mean much as a designation anymore, because the majority of active players are probably now by default "fighters". Mining is not used much, I think, and when I see it used, it's mostly referring to mining special goods in the Space eras such as Space Age Mars.
And there you have it, a brief history of "fighting", "farming", and "mining" in FoE. (Other long time players, feel free to augment/correct this description.)