are both within the Schengen zone. You had to present your papers when you first entered Continental Europe (via Amsterdam?) and you will likely have to present them again when you leave. You don't usually have to present them within the zone again unless there is some kind of a spot check in exceptional circumstances or some situation.
Here's the Schengen area: https://en.wikipedia.org/wiki/Schengen_Area
The UK, which you mentioned earlier, is not part of the Schengen zone. It is, however, part of the EU. Switzerland, where I have lived for the past 20+ years, is not part of the EU. It is, however, part of the Schengen zone. Neither the UK nor Switzerland is part of the Eurozone.
It does make one's head spin a bit.
A long-time US expat friend who has residence in Thailand (mainly for medical reasons), but who has spent much of the past couple years subletting in Paris flew from Paris to Thailand via Helsinki last year. She had no trouble boarding her plane to Helsinki in Paris, but when she tried to board her flight from Helsinki (the Schengen zone departure point), she was stopped, questioned, and ultimately received a stiff fine (several thousand Euros) because - unbeknownst to her - her French residence had gone beyond its validity point. She had been under the mistaken impression that traveling from France into Switzerland would count as leaving the Schengen area for an automatic renewal. It doesn't since Switzerland is part of Schengen.
They did finally let her leave from Helsinki but informed her that she would not be allowed to re-enter the Schengen zone again at any entrance point until she had resolved her residence situation with the French consulate in Thailand. Much of her short visit in Thailand was spent in completing paperwork to re-enter Europe.
That was a lesson she will not soon forget.
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