What makes a third or fourth wave of feminism different from the first two?

The First Wave is your Susan B Anthony/Marie Stopes era stuff, seeking to redress a variety of manifest injustices, most notably the right to vote. It started in the 19th century and could be said to have ended with the right to vote in the 1920s (in the US).

The Second Wave started in the 1960s, though "feminism" never really stopped from the First Wave. This was the Betty Friedan/Gloria Steinem era; it was also called "Women's Liberation". It focused on expanding women's roles from the traditional wife-and-mother thing to, well, everything else: the right to equal pay for equal work (and in any job), the right to do what they wanted with their bodies, an end to all sorts of sexism and discrimination. I would say that it ended with the failure of the Equal Rights Amendment, part of an anti-feminist backlash that eventually turned to infighting. It was, however, hugely successful in advancing the rights of women to be treated equally in work, in politics, at school, and in society at large.

The Third Wave is more nebulous. It doesn't have a strong legislative agenda, and the key players are less likely to be household words. It could be said to have begun as soon as the Second Wave ended, trying to pursue remaining legal injustices, but it seems to me to be more about expanding and questioning received notions of gender and gender roles. It is more abstract and less politically focused; it's more academic and post-modern. I'd say that the political aspects of it are really Second Wave feminism continuing to work on the remaining problems.

The Fourth Wave is a Quora board. It's not really a broader movement at all (yet), except as an attempt to try to get past some of the divisiveness and lack of focus that marked Third Wave feminism. It seeks to solve the remaining very real issues that gender still leaves in our nation, as well as the rest of the world, much of which still hasn't benefited from the gains of the First Wave.