The difference is clearer when you say: Japan's people. Japanese people. The difference isn't so obvious with the word "economy" as the two are essentially the same.

Japan's economy -> is the "Saxon genitive" form and it's used to express possession when the possessor is an animate being.

Japanese <- this is an adjective in this case. You are describing a noun that comes after it. noun + 's <- This means possession. What comes after this belongs to the noun. "Japanese flowers". Flowers that are Japanese. They have Japanese characteristics. "Japan's flowers". Flowers that belong by Japan. They don't necessarily have to be Japanese flowers. Adjective: Pretty flowers, ugly flowers, Japanese flowers. Possessive: My flowers, your flowers, Earth's flowers, Japan's flowers.