Crime is generally considered to be the violation of someone else. Either their life, liberty, or property.
There is also "victimless crime", which can't actually be a crime. This is mainly what The State seeks to control and punish.
"Crime" is just anything the government doesn't approve of. It could be right or wrong, or even morally and ethically neutral. Many hideously evil acts are not "crimes" if they are committed by government agents, and many truly good things are "crimes" just because the government says so.
The State commits actual crime, while pretending it doesn't, and punishes "crime" while pretending it is protecting "society".
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