Spoiler: Japanese teachers say, there is no difference. Westerners argue.
Let’s look at Japanese words first and give a translation. (I need to show off and prove, that I didn't get my degree in Japanology for nothing, right?!)
Shibari 縛り - this noun is coming from the verb Shibaru, which means to tie (anything), not exactly in a pretty way. Kinbaku 緊縛 - tight binding. 緊 kin — tight/tough, 縛 baku — binding—same kanji (character) that is SHIBARU.
Japanese masters say that shibari is any binding or restriction, and kinbaku means only Japanese rope bondage. Short and easy. The word kinbaku is younger and was specially invented to mean exactly Japanese rope bondage.
Hajime Kinoko says that shibari and kinbaku are the same thing. In Japan, these words are equal, people use both. If you speak with ignorant people, the word kinbaku will be more appropriate, because it will be more accurate.
Western masters say, that shibari is more about what is directed outward (aesthetics, patterns, shows), and kinbaku is about what happens between partners. Shibari — just tying, kinbaku — having an actual emotional rope session.
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