Kinbaku

Generally understood to mean a style of Japanese Bondage. Sometimes used interchangeably with Shibari but also highly discussed as being distinct from one another. Kinbaku is a subcategory of Rope Bondage.

Kinbaku vrs Shibari

Both terms are used interchangeably as the older term for the bondage itself is Kinbaku (source) but Shibari is an even older word which means "to tie" in Japanese (source) so both are considered correct. Shibari is considered a more modern and westernized term and is in more frequent use.

The words do have slightly different meanings with Shibari meaning "To tie" and Kinbaku meaning "in a tight way tie securely" (source). Thus sometimes Kinbaku is used to refer to the more restraining ties where as Shibari is used for ties that do not by definition restrain.

Some describe differences between the two terms as Shibari being artistic vs Kinbaku being sexual (source)

Bakushi have commonly used the terms interchangeably in classes, interviews and other media.