LOTS of differences between USGA and R&A (also CONGU) handicapping systems. Two important differences (if I remember correctly):
1. As phb said, USGA uses best 10 of 20 differentials. They are trying to measure golfer's 'potential' vs. actual average. R&A is more likely to be closer to an average.
2. Only tournament/competition rounds count in R&A handicapping, where any round played by the Rules of Golf counts in the USGA system.
Plenty of other differences as well (google can probably tell you more). One other thing that's important, low handicappers can actually win handicapped competitions under the R&A system (and often do). Under USGA system, they have no chance.