I'm mostly talking about 13-man, 3-scum setups and 9-man, 2-scum setups.
Majority Lynch requires over 50% of the players in the game to vote someone in order for the lynch to happen. For example, with 9 alive, you need 5 votes on someone to lynch them. If the vote leader has 4 or fewer votes, no lynch happens.
Plurality Lynch lynches whoever has the most votes, even if it's not a majority. So if 9 people are alive and the wagons are 4-3-2, the person with 4 votes on them gets lynched.
For the most part, after D2, Plurality and Majority lynch are the same. During D1 and D2, it's possible for town to have a "Minority Plurality", where the lead wagon doesn't have a majority, and for scum to be unable to disrupt that. In a 10 vs 3 situation, town could concievably lynch scum with like a 6 or 5 vote wagon, if scum can't easily pile onto a counterwagon. Obviously this is leaving out the idea of scum bussing, but on its basics, plurality is definitely different from majority during D1 of 13p mafia.
If town mislynches twice in 13p, though, we end up at 6-3. At this point, if it were majority, town would need 5 votes to lynch. In plurality, however, town probably ALSO needs 5 votes to lynch. If town splits 4-2, scum can in theory pile onto the 2-vote wagon and win. In 4-3 (or any) LYLO/MYLO, of course, Town needs to vote all together with a majority.
What we see is, the more wiggle room town has in terms of mislynches, the more plurality diverges from majority. In 9p minis (7-2), if town mislynches once, we're at 5-2. In majority, town needs 4 to lynch. In plurality, town also "needs" 4 to lynch (Again, disregarding bussing) because with only 3 votes scum could push a counterwagon over the top with a badly placed vote or two from a townie.
I think, actually, the big impact of Majority is on counterwagons and side votes. People will take flak for not being on one of the two main wagons as the day goes on, and there will be fewer shenannigans, for better and for worse, during the early games.
Majority is probably best used in a smaller games, where plurality is a lot like majority in terms of punishing town for not voting together, or in Instant lynch games, which are hilarious and awesome.
What do you think?