No. SBAS is an augmentation system, but it's not identical.
Differential positioning is pretty simple in concept. If you have a single receiver at a known point and a nearby receiver, the first can record how it is receiving the signals and compute an offset between when the signal is expected and how it actually arrives. This offset is then sent to the nearby receiver and is applied to the incoming satellite signals.
Any source of delay that is common to the two receivers is therefore removed. But you need that nearby receiver, so it doesn't scale up to cover a large area easily.
The SBAS in use in the US (WAAS) uses a different technique. Although there are multiple error sources in the signal, the largest one is usually the uncertainty in the delay due to propagation through the ionosphere. The depth and density of the ionosphere changes on somewhat short time periods. At the same time, just like a large weather system the state of the ionosphere is correlated between nearby locations.
WAAS uses a network of reference stations throughout the US. Each one records the current offset of the received signals and uses that to estimate the ionosphere delay. Then all the information is combined together to form a model of the delay everywhere in the US. This model can then be compressed and sent via another satellite. Any receiver in the target area can now get increased precision and also updates about any particular satellites that are sending unusable or incorrect data.
Similar SBAS systems are available in other areas of the globe (like European EGNOS.