You're thinking of Extreme Programming (XP). Many of the Manifesto group participants came from that camp. You might say that Agile is mostly based off of XP as a result, although Schwaber is certainly among the signatories.

Kanban comes from the manufacturing world. You might find some overlap with Agile, but is not directly associated. Agile is abundantly clear that it is about software.

And yes, if you want to be pedantic, it might be more accurate to say that Agile is a generalization of XP and Scrum, rather than XP and Scrum being formalizations. Agile was written after. But I'm not sure that changes the intent of the original comment.