The Australian swag has been around for a long time but not in it's current form. Swags, or swag bedrolls as they are also known, are becoming the must have camp bed for camping, fishing, outback adventure, motorbike clubs, school camps and staying overnight at friends.
Traditionally they were used in the outback as a travelling bed roll by the station workers (most have heard the tale of the jolly swag man) but more and more they are becoming used by city folk interested in a weekend fishing trip who want a quick, easy, tough roll out bed that protects them from rain and midges.
Essentially the modern swag is a thin tough mattress in a canvas wrap around, sometimes with insect meshing where the vents are.
They differ from tents in two aspects, the first being that the swag is usually made from canvas whereas most tents these days are made from nylon which doesn't breathe. This means that in rainy weather when you are inside your swag there is no build up of heat and condensation as happens in closed in nylon tents. The second difference is that swags are a lot quicker and simpler to set up (or at least they should be).
There has also been a shift in swag making away from the traditional heavy cotton canvases of the past fifty years which, when wet, became very heavy. Your modern swag is likely to be made from the new industrial canvases being made in Australia which combine lightness with strength.