They are absolutely not the same. e.g. the Cornell method is for learning.

> Do you mean the idea that hand movements of writing help retention?

It's not just that, but also mentally engaging with the material.

The former is, e.g., writing down how you got some software working on your machine so you can reference it in a few years.

I think more the idea that wrestling with new ideas and distilling them down can you help you to understand something, even if that note is then immediately thrown out. The purpose of the notetaking in this case is not for future reference.