Green Tea originated in China, but are often associated more strongly with Japan.
There's a world of difference between them in both looks and taste. If you've tried a generic 'green tea' from a bag, it's most likely to be of Chinese origin.
Green teas are leaves that have been plucked, withered and then either steamed or occasionally roasted to ensure no fermentation occurs.
Japanese teas tend to fare better when prepared with a shorter steeping time and a cooler temperature otherwise you may find them too bitter. Steeping time and temperature varies with different teas, generally, lower-grade green teas are steeped hotter and longer, whereas higher-quality teas are steeped cooler and shorter.