The picture you posted looks like a removable compensator. Sometimes a non-ported cap is also available for guns so equipped. Nothing like that is available for a 360PD, but they can be Mag-na-ported.
This shows a two piece barrel. The shroud is the alloy outer piece, the barrel is the rifled threaded pipe. S&W won’t sell the wrenches, so why buy a shroud? Plus these are covered by the lifetime warranty.
These guns also have a shrouded ejector rod as part of the barrel shroud and Bodyguards have a shrouded hammer. It can all be very confusing.