Kaizen focuses on continuous improvement for quality, productivity, safety and other areas. International standards like ISO 9001 (Quality Management System - QMS), ISO 45001 (Occupation Health and Safety Management System Standard - OH&SMS) also talks on improvement in Clause 10. Kaizen talks about continuous improvement whereas ISO 9001, ISO 45001 specifies requirements about continual improvement.
The ISO 9001, ISO 45001 improvement is related to systematic improvement in quality management system, health and safety management system respectively. Whereas Kaizen improvement is related to Lean methodologies, Quality, Production and Safety, it also counts small improvements or daily workplace improvements as well.
Continuous improvement means that organizations are constantly looking for small-scale improvement in everyday workplace practice apart from Kaizen stories and themes. The workforce at the floor is daily improving by taking small initiatives of Kaizen or continuous improvement. For example, even having a marked waste bin is also considered as a Kaizen. However this approach has not been adopted by the international standards like ISO 9001, ISO 45001 for management system-level improvements instead the standards use the term continual improvement or simply as an improvement.
The term "Continual" specifies time span that encompasses over an extended period of time, but with due breaks of interruption. The International standards like ISO 9001, ISO 45001 uses this term as the standard making bodies have realized that improvement at management system level cannot be continuous. An improvement at the management system level will be incorporated and then it has to sustain for a period of time to check its effectiveness. It is not possible to improve at management system level daily or weekly. Internal audits and management reviews are planned at defined intervals. At the management system level, internal audit and management reviews play an important role for improvement but after the due interval.
Logically any improvement to be sustainable needs to follow a continual improvement process instead of continuous. Although the Kaizen methodology uses the term continuous as the methodology emphasizes on sustaining the improvements made, therefore it will be better to name it "Continual" instead of "Continuous".