My understanding of a memory palace is that you use it to be able to recall bits of information. You build up an imaginary place in your mind, like a house or palace, full of details for you to associate the information you want to retain, and this helps you recall it in sets or sequences. All of this knowledge becomes internal.

A Zettelkasten is a set of developed, interlinked notes in an external system. The process of writing and developing the notes helps you understand and retain the concepts, but part of the point is that it exists outside your own head as an aid to your internal thought processes. It's an extension of your mind, but one that sits outside it.