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They're all supercharged and as said there's no reliable way to visually tell them apart from the outside. To be sure, get the VIN and get the build spec online or through a dealer.
You can also check if there's any photo of the engine compartment. That's one place where you can see a difference. The 380 / S has the adaptive suspension which has small cables connected to the tops of the shock absorbers. Don't know if the base car possibly also could have that as an option but I've never seen a base / 340 with it.
Sweet, that's the quintessential and perfect F-Type spec then, provided that it's also decently equipped. Being a 380/S it already has all the important stuff.
There are more agile but less powerful and less characterful versions, there more powerful but less agile and less characterful versions and then there's the RWD 380/S.
Good luck with the purchase if you go ahead with it!