As a Nordic citizen living or working in Denmark you earn an entitlement to a Danish social pension if you meet the statutory requirements. In Denmark you can earn the entitlement to the old age pension or early retirement pension. Entitlement to a social pension that you have earned will be paid when other statutory requirements are met. Payment can take place even if you do not live in Denmark.
ATP is the abbreviation for the Supplementary Pension and is a statutory benefit that is normally paid in addition to wages so that you as a Nordic citizen have the opportunity to earn a supplementary pension for later payment.