Rescue: Temporarily houses animals until new homes are found while ensuring their immediate safety, typically those with medical or mental problems who aren't suited for life as a household pet but can be rehabilitated
Humane Society: Works as shelters, typically focusing on adoption; many are "open admission" facilities that will accept almost any animal but euthanize many; often work closely with the government
Animal Control Agency: Governmental-run and is often responsible for animal cruelty/welfare calls from the public, investigating, impounding pets running without license or rabies tags or are abandoned