Schengen has nothing to do with this. Schengen is only about immigration controls on persons, not sales taxes and duties on goods or the movement of goods.

Switzerland IS part of Schengen, however it is not part of the European common customs and VAT area. (Nor is it part of the EU, although that is also irrelevant)
The UK and Ireland are both part of the European VAT area, but they are NOT part of Schengen.
Spain is part of the EU and Schengen, and the mainland is part of the VAT area, but the Canary Islands and her North African enclaves are NOT part of the VAT
area, although they are part of the EU and Schengen like the rest of the country.

As you can see, Schengen is irrelevant to the question of VAT, as is the EU.
The question is whether you are part of the customs union area.


Accordingly, although the setup can vary by airport and country, you can easily have people flying inside the schengen area, but leaving/entering the customs union. Or people flying within the customs union, but leaving and entering Schenegen.

As such, in non-schepgen areas of airports, goods may be sold with a VAT element being collected on passengers staying inside the customs area, but without any Vat being collected for passengers travelling to outside the customs area.
This will usually be governed by boarding pass where it is happening.
Sometimes prices will differ, other times they will not.

I certianly remember, relatively recently, seeing both vat inclusive and exclusive prices on display on high value items in ZRH airport. I can't remember how they do low value items (if it is common pricing or not).