While job hunting in Europe I came across the term European work permit. Can I only get a job in a European country if I have such a European work permit?
There is no such thing as a European work permit! For each European country you need to apply separately for a work permit. Nationals of the European Union member states (including Iceland, Norway and Switzerland) are able to work in any other EU member state, exercising the same rights as nationals of those countries. However, non-EU job seekers with for instance a work permit for the UK are not allowed to work in Italy, Germany, France or any other EU country. The only exception under certain circumstances is short-term contract work. Please note that the European Economic Area (EEA) countries all – except Luxembourg – have signed the EU treaties regarding labour mobility, thus in all EEA countries freedom of movement of EEA workers is allowed, similar to the EU (European Union) member states.
