Most Jag's that folks here in the states first encounter are the type that you see in your basic "Outers" cleaning kit. Plastic, sharp pointy tit on the end and the 'barrel' of the jag is almost bore size. Your place the patch (hopefully the correct size) on the muzzle of the weapon and jam the sucker through. And it would clean the be'jeezus out of the bore - if the patch was sized correctly!
The jag that you are refering to is used in just about the manner that you mentioned. The regular sized patch is wrapped around the jag so that the edge of the material is inline with (parallel to?) the center line of the bore. This type of jag is size sensitive too, but it does a better job of cleaning as it fits the bore better, and it brings more patch surface into contact with the bore - more uniformly too.
I first saw one of these Jag's used with my friends Walther Air rifle. It came with the cleaning kit that arrived with the rifle. Works like a charm, and I recommend getting them for your rifle if you can find them. I thing I got mine from Natchez Shooters supply, and Brownell's should have them too.
Good Luck, Unkel Gilbey