In Norway, each employee freely chooses their union. It is common in some industries that people belong to several different unions, and that some are not part of union. And usually they are based on particular profession, like engineering or economics. Unions then have more a passive role, offering services like free legal representation, better insurance deals, and training.
Only some areas like teachers seem to have near-homogeneous membership and unions taking an active role. And this seems mostly to be because 90% have the same employeer - the state (public education). Because of standardized working terms (incl salary), they have to be negotiated centrally.