More than semantics!
Which is the right (relevant) "strategic" question to ask EUropeans? a) "Do you trust the EU?" or b) "Do you like (or love?) the EU?"
The term "European" denotes geographical identity, analogous to Asian, African (let's leave "American" aside for now). Thus a term such as "EUropean" or something should be used to denote those who are and feel positive about being citizens of the European Union, which after all, does not and probably never will include ALL European countries (eg Norway does not want to join).
All institutions of the EU should be renamed to reflect that distinction properly, eg EU Commission, EU Parliament, EUCJ, etc!
Plus, IMO, the biggest conceptual fuzz relates to what the term "EU" denotes in people's minds. "EU" is not its (ie the EU) institutions, everything in the European Union is (& should be perceived by the people as) "EU"!
Eg does one ask a German "Do you trust Germany?" Makes no sense as a question!
Lastly (for now):
Case in point: "EU Affairs" vs "European Affairs".