Someone has pointed out that my use of "civil offence" and "criminal offence" makes sense in Ireland but not in Belgium.
The distinction I was making is between breaches of the law that are investigated by the police/government regardless of whether someone's filed a complaint or not, and breaches of the law that the police will only investigate if there is a complaint.
Murder is an obvious example of the former, and slander is an obvious example of the latter.
In Ireland, the former is called a "criminal offence" and the latter is a "civil offence". In Belgium, they're both called a "crime", but one is an "automatically enforced crime" and the other is "a crime that is only enforced when there is a complaint".