Yes they are definitely post-2.1, possibly after a later patch, I noticed them after some time. They are regular missions except the text says they will help in the war - but I don't know if this is true or not.
The mission text now reflects the state, and by observation, so do mission types (largely). So if you are in election, you will get text from the mission giver saying something about elections (in all systems the faction is present in). Same with Boom and War. The types of mission alter slightly - so when at war you get regular missions, plus combat. In election you get regular plus a bunch of data missions (deliver poll data) or retrieval missions (retrieve diplomatic info) and the like. In Boom, you obviously get more trade type missions.
I quite agree with Sentenza; I am not sure how effective these specialised mission types are, or not. Particularly when they pop up in systems the faction is in, but where the war or election is not actually taking place. For example, we have found combat missions to have minimal effect in war - far better to just do the combat zones (although the missions help the pay-out); don't rely on missions alone. Likewise in election, the specialised missions don't seem to be having a significantly different effect to regular missions and/or other methods of raising influence. However, we have not been scientifically testing this stuff; our systems are too well trodden to really attempt proper testing. It is simply observation of the day to day influence change, having knowledge of what we have done, and then trying to deduce general truths from that.
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EDIT
so as goemon said - it is just flavour text. Stick to the established methods - combat actions in war, trade in boom, and so on. Certainly this has served our group well thus far.