The difference can vary from company to company.
Green Belt training can be anywhere from 3 days to 9 days, whereas black belt training can be anywhere from 2 weeks to 4 weeks. Good training should be 2 weeks for green belt and 4 weeks for black belt. Green belt should cover the DMAIC methodology, basic statistics, MSA, capability studies, control charts, graphical data exploration and possibly basic hypothesis testing. Black Belt training will typically add design of experiments and regression analysis and more emphasis on improvement tools.
Green belt projects also vary a lot from company to company. Some are handled as described by optomist1, while other companies will have green belts run their own projects. These are usually tightly scoped projects focused on a simple process or operation and can be completed within 3 - 6 months working part time. A black belt project is typically broader, including more complex processes, can be completed in 6 - 12 months working full time. Enterprise-wide processes are usually reserved for master black belts.
I am and have been a master black belt in my company since 2008.