The game of "base-ball" has been around since Tudor times and was initially codified by the GAA (Gaelic rules). When it was exported to the USA it became known as Massachusetts rules and that is where softball and baseball come from. Instead confusingly rounders is actually more similar to "British baseball", which is still played in Wales and the north, but I don't know a lot about it.

Rounders you have a small, one-handed bat. The bases are poles. Terminology seems to be more like cricket (bowled, stumped, etc). You score a rounder by getting to the 4th pole on your bat. If you get to 2nd or 3rd pole it's 1/2 a rounder. You get the batter out by catching the ball in the air off the bat or by touching the pole they are running to. You only play 2 innings normally because everyone one on team bats and then it switches over (also like crIckes). I don't know a lot about rounders because I have never played it (I believe it is mainly played by girls in schools).

Baseball is quite different. You have 9 players per side (pitcher, catcher, four infielders and three outfielders), three square bases and a uniquely-shaped home plate, all 90ft apart. The ball is small and hard. The bat is much larger than in rounders and you use it two-handed. The pitcher throws from a raised mound 60ft6in from the home plate. You usually play 7 or 9 innings, but once three batters are out you switch sides. You can steal bases by running to the next one as the pitcher starts his wind up. You can bunt the ball down on the ground to try to advance runners (known as a sacrifice bunt). This is played at all levels predominately in North America, Japan and Latin America.

Softball is a variant on (American) baseball. I play slowpitch but there is also a fastpitch version. Slowpitch does not have stealing or bunting but fastpitch does. The balls are larger than baseballs but not soft as you would imagine from the name! They will still hurt when they hit you (as the attached picture from this weekend will attest). 11in diameter for women and 12in for men. The bases are 65ft apart as opposed to 90ft for baseball.

I play mainly co-ed softball which is mixed men and women but you must have the same number of each. If the pitcher is M then the catcher has to be F, and vice versa. Two men/women in the infield and softball has four outfielders, two of which must be F too. The batting lineup must alternate sexes too, so you cannot have two men or women batting consecutively. I have also played single sex in a male-only team. The only real difference is that in co-ed if you walk a male batter (throw four pitches outside of the strike zone) then he gets two bases instead of the normal one (this is to stop dubious tactics of walking the male on purpose to get to a perceived weaker female batter).

There are a lot of other minor differences but I'm sure you're already regretting asking.