The skinny Buddha was born Prince Siddhartha Gutama in India, and searched for the solution to the problems of disease, old age and death. In his quest he became ‘awake’ and laid out the the Four Noble Truths and the Eightfold Path as the solution to the problem of suffering and the path to enlightenment.
He is the founder of the philosophy of Buddhism.
The fat one, usually very happy and laughing, is not ‘the’ Buddha.
In China, his name is Budai Luohan, a Chinese monk, believed to be an earlier incarnation of Matreiya the future Buddha.
In Japan, his name is Hotei, the god of contentment and happiness, and the god of good luck from Shintosim.
He is generally depicted carrying a large cloth bag over his back, one that never empties, he uses it to feed the poor and needy.
The Japanese spelling of “Ho Tei” means “cloth bag.” He also holds a Chinese fan called an oogi (said to be a “wish giving” fan, this type of fan was used by the aristocracy to indicate to vassals that their requests would be granted. Hotei is most likely based on the itinerant 10th-century Chinese Buddhist monk and hermit Budaishi who is said to be an incarnation of Miroku Bodhisattva (Maitreya in Sanskrit).