In my piles of random hardware I have a pile of brass compression fittings for water lines. I have two different types of compression nuts. One has a sleeve inside it. The other doesn't. What's the difference?
The one on the left tightens the "compression ring" around a (usually copper, but could be plastic) tube. The one on the right tightens itself onto the "coned" (sorta' phallic-shaped) end of a pipe.