DIN was replaced by ISO, i.e., a domestic standard was replaced by an international one. So was ASA-it's just that ISO numbers match those of ASA.
ISO has often adopted current standards instead of inventing new ones. For example, the original ISO 9000 quality inspection standard for manufacturing was, when adopted, word for word the then-recently-canceled U.S. Military Standard I-45.
Actually, ISO incorporates both ASA and DIN: ISO 100/21° (or very similar).