Refers to housing developed by public corporations, especially the former Japan Housing Corporation (日本住宅公団). Often implies apartment complexes or danchi.
彼は公団住宅に住んでいる。
He lives in public housing.
団地 is a broader term for a housing complex or estate, which may include public housing (公団住宅) but also privately developed complexes.
公営住宅 is public housing provided by local governments under the Public Housing Act, typically for low-income households, while 公団住宅 was developed by the now-dissolved Japan Housing Corporation.
Formed from 公団 “public corporation” and 住宅 “housing,” originally referring especially to housing supplied by a government-established public corporation.