What they have in common is meaning. =)
Basically, in ye olden days of prehistory, Japan had its own spoken language but no written language. When Buddhist scholars arrived from China, they brought the Chinese writing system with them, and it became kanji. Chinese characters were used to write Japanese words which already existed, so the Japanese pronunciation was attached to the Chinese characters. This is the kun’yomi. However, the Chinese characters also came with the Chinese spoken language already attached to them, so these readings were added to Japanese as well – this in the on’yomi. Thing is, both readings referred to the same word. Or at least, they did at the time – etymology has probably changed a few things in the intervening centuries…