Little league (age 12 and under) is played on a 60 foot diamond (60' between bases) and a 46' distance from the pitcher's plate (the rubber) and the back of home plate.
Juniors and above (age 13 and up) play on a 90 foot diamond and 60'6" pitcher's plate to home plate, the same dimensions as Major League Baseball.
That's a big jump for the 13 year olds, and games early in the Juniors year are painful to watch, with 3rd basemen and shortstops 2 hopping throws to first, and pitchers not able to reach home plate in the air.
Intermediate baseball (often called 50/70) fits in between Majors and Juniors, where the bases are 70' apart and pitcher plate distance is 50'. Players in Intermediate are aged 11-13, and in most leagues are allowed to play both Majors (11, 12 year olds) and Intermediate. The Juniors rules are in effect (leads, steals, balks, 2 1/4" or 2 5/8" bats) giving the kids a chance to experience the big boy rules.
The Intermediate World Series is held in Livermore, CA in August.