My ask is less about segmenting tagged content and more about preserving the URL from my existing structure. For example if I used different tag name for my blog post than for my page posts I would end up with the following.
http://example.com/blog/
http://example.com/pages
http://example.com/ctags
http://example.com/ptags
When what I want is
Taxonomies are global, and their URL to their index page is rooted at the site root. I want a taxonomy that is rooted at /blog
Edit: to clarify I am also looking for individual tags, not just an index page for all tags:
http://example.com/blog/tag
http://example.com/blog/tag/cats
http://example.com/blog/tag/dogs