Monoshock, older style, regular swingarm
In 1977, the first monoshock system appeared to niche markets and racers. It has actually been around in one form or another since the 1930's, but it was only in the early 80's that monoshocks started to appear on production bikes. Monoshock is actually a Yamaha trademark, but it has become synonymous with the design in the same way as people in the UK refer to vacuum cleaners as hoovers. (The Honda version is called Pro-Link). The premise was that manufacturers could save some weight by redesigning the rear suspension and removing one of the coilover units. Monoshocks are still coilovers, but there's only one and it's mounted centrally to the swingarm. On earlier models, the rear swingarm was a sort of basket with a linkage at the top-front. The monoshock sat nearly horizontal in the bike.
You can read more and see diagrams in http://www.carbibles.com/suspension_bible_bikes.html