Swags (as far as I know) are pretty unique to Australia. Started with Cattle drovers back in the 1800s and the 1900s. Even today to a lesser extent used by drovers. Those days it was more like an oversized canvas sleeping bag. The canvas kept them dry from water and the cold​d conditions of the outback.

Today many overlanders still like the swag but designs have evolved, more aimed at the recreation market. The main difference to a dome tent, swags are made from canvas, comes with a mattress and accommodates no more than two adults. Some designs can take two adults and two children. Unlike in some dome tents, it is not possible to stand up in a swag.

I guess the main attraction for swags over tents is it's canvas construction (works well in cold desert conditions) and it also in part a sense of Aussie outback tradition.