Question

Difference between buddha and laughing buddha

Answer 1

HOLA!!!!!!!!!!

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By fat Buddha, I assume you're talking about Budai, or as famously known the Laughing Buddha.
I am also assuming that you are referring to Gautam Buddha, the founder of Buddhism as the regular Buddha.

Laughing Buddha, or Fat Buddha, or Budai is believed to be a matter of Maitreya, a Bodhisattva, who will appear sometime in future, gain complete knowledge, and guide people to dharma when they all seem to have forgotten it.

Gautam Buddha, the one you are referring to as, 'regular Buddha' has already been born, achieved knowledge, and died. He is the founder of Buddhism and the 25th Bodhisattva of Buddhism. He led people on the path of Dharma. 

Basically, they are two different people, one already born and dead, other yet to be born. 

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Answer 2

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Some Buddhist traditions consider him a Buddha or 'Bodhisattva', usually Maitreya (the future Buddha). His large protruding stomach and jolly smile have given him the common designation “Laughing Buddha”. In Japanese, 'Budai' is pronounced as 'Hotei'. It means 'clothsack' or 'glutton'.