When we talk about a drywall sanding sponge we could be talking about more than one thing. Originally, a sponge was used to 'wet sand' the drywall.
Water can be added to a standard household sponge and the sponge willl smooth the drywall. Saying that you are sanding is a bit of a misnomer, the sponge actually dissolves the drywall mud. This makes it easy to groove or otherwise remove too much of the finish.
Sponges That Actually Sand
A few years ago, the technology came out that allowed abrasive type sponges to be created. The plastics or polymers used are similar to your plastic pot scrubbers. They are tough and last as long or longer than the equivalent sand paper.
For drywall they are ideal, since drywall compound is fairly soft and it does not wear them down too quickly.