"Buddha" is a title, not a name. The original Buddha with a capital B lived in India, but since then other men have achieved... um... "buddhahood," and they are lower-case buddhas.
Until the last few decades, most Americans only knew about Buddhism through information from China. That's where, perhaps, the majority of the modern world's Buddhists live, and in addition it's a country whose culture has spread widely through commerce, particularly in the USA. Most Americans have eaten in a Chinese restaurant run by Chinese people and decorated with artifacts of Chinese culture, with a big fat buddha statue near the door.
Hotei was a Chinese man who lived around 950CE and achieved buddhahood by, among other things, practicing charity. The Chinese buddha image is modeled after Hotei.