It's one thing when folks go around claiming "kaizen is the Japanese word for 'continual improvement'", but another when they decide to just invent the corresponding etymology.
From a "life transformation" website:
The Kaizen philosophy is drawn from the Japanese word kai which means “continuous”
NO. The kai half of kaizen does not in any way mean or even suggest "continuous". Nor is it a "word".
and zen meaning “improvement” or “wisdom”.
NO. You're just making this up.
The real kaizen 改善 is a Chinese word that has been adopted into Japanese and Korean (and possibly other languages). Its first character kai 改 carries the general meanings "reform, renew, change, make". Its second character zen 善 carries the general meanings "good, virtuous". Together, they suggest "change for the better" or simply "make good" – what we in English would call "improve" or "improvement".
And that's what kaizen means, whether etymologically, in Japanese dictionary definitions, in Japanese/English dictionary definitions, or in actual usage in Japanese. No "continuous" and no "Japanese philosophy". Just "improve/improvement".
There's lots more detail in what is currently this site's most popular article:
There. And now you know a new thing today!