I use the internal tags (aka the ones with hashtags) to change the layout of posts on the front page and on the site page itself. This screenshot from my front page differentiates the two. Articles with the “#blurb” tag use static images, have slight text changes, and have small text tags on top; articles without use animated GIFs and are more red in color.
The pages with “#blurb” are more stripped-down in style as well, using a gray background, rather than white.
I used somewhat similar approaches back when I was using Tumblr for my main outlet.
The benefit of the internal tags is that I can still use regular tags for contextual/SEO reasons, while the internal tags are strictly focused on organization and navigation.