Yes, although the R9 380 is a rebrand, it uses a newer GCN GPU than the 280X, which in turn is a re-branded 7970 Ghz. The R9 380 uses the GPU found inside the R9 285.
I would recommend going for the R9 380 4GB because of 2 reasons: 1.- the bigger amount of RAM will come in handy down the road with new games and higher resolutions, plus it does have additional tweaks that the 280X doesn't have, and 2.- is because you have FreeSync and the Audio thingy as bonuses. Performance wise, the 280X should edge out the 380 in some scenarios, but in an overall picture, the 380 should be the better buy IMO.
If price is a concern and the "other features" are not an interesting point for you, just get the cheaper option. Both will do a good job...