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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?
They both do the same thing except the one on the left has an integral compression ring (ferrule) and the one on the right uses a separate ferrule (which is not in your picture).
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.
Required, but never shown