Three institutions, different sources of authority
The Commission normally initiates legislation. The European Parliament represents voters directly, while the Council represents member-state governments. Under the ordinary legislative procedure, Parliament and Council are co-legislators and both must approve the same text.
That structure means 'the EU decided' can conceal a long bargaining process involving institutions with different constituencies and incentives.
Most of the power is exercised before the final vote
A proposal moves through parliamentary committees, Council working parties, Coreper and negotiations between institutions. Compromises can be reached at first or second reading, and conciliation exists when the co-legislators cannot agree later in the process.
The final vote is therefore often confirmation of a bargain whose details were shaped earlier by rapporteurs, national representatives, officials and negotiators. Following only plenary votes misses much of where practical influence enters the process.
Not every EU decision follows this route
The ordinary legislative procedure covers most EU legislation, but treaties provide special procedures in some areas. Voting rules also vary. Foreign policy, some tax matters and other sensitive fields can require unanimity among governments, producing a different distribution of power.