Well, in Italy postcodes define city areas, and cities, for example for my city the main postcode is 80100, but my area is 80142, and it contains few buildings, so it's different from UK, UK was the first time I saw such specific postcodes, and I've lived also in Germany and Netherlands

Netherlands had a postcode per street

Oh yeah, I remember being able to insert just postcode and street number in forms, but it's not as specific as UK, I think

Odd numbered homes on one side of the street and evens on the other often have different postcodes

Many buildings also have their own postcode! (The second half of the postcode represents the 'delivery point' which is basically limited by the amount of post that the postman/woman can physically carry...)

Postcodes are about sorting mail to match the delivery rounds.