The Campania Express is just a not-so-special (more on that latter) operated by EAV, the same company that operates commuter trains to Sorrento and other lines. EVA was formerly known as "Circumvesuviana", which is no more (since 2016 or so). You still see some "Circumvesuviana" train signs though (it refers to railway lines, not the specific type of rolling stock).
Now here is the thing: when first introduced many years ago, the Campania Express was the only air-conditioned, modern train option between Napoli and Pompeii (or Sorrento).
Now, the only real differences between "Campania Express" and regular EAV trains are: (1) they don't take passengers standing (only sell reservations for as many seats are on the train); (2) the trains are slightly faster (just some 13 min or so). Because EAV has been replacing its rolling stock, most trains on the Sorrento line are otherwise identical to the "Campania Express".
So because these tickets are cheap, and the timing convenient, I'd buy the Campania Express at 11:39, but not be much bothered in case something happens. You then buy spot tickets to other regular trains.
39 minutes is plenty to change between the high-speed train platforms and the underground and rather claustrophobic EAV platforms. "Porta Garibaldi" station is just the name of the underground sector of the same large station-building complex.
