If you need to show different navigation list for different pages, then you can create different layouts for the pages and add page specific navigation list snippets to those layouts. More information on how and why the pages are different, some light on the business case for this requirement can help in coming up with alternate solutions as well.
Just FYI, visibility can be set on snippets enclosed in containers. But the containers are to be enclosed in a Data View of any object with attributes like Boolean or Enums to handle visibility.
Biggest question here is: what is defining the difference?
If it is based on data, then it should be in a data container.
If you just what to show a different layout of the list view, then you shouldn't work with a snippet. The idea behind a snippet is that the content of the snippet is everywhere the same. And can be maintained in the single snippet. Thus showing the content of a snippet differently depending on the page is contrary to the concept of a snippet