Exactly which types of living quarters are classified as group quarters (GQ) varies by census year, and also depends on the exact characteristics of each facility. For the 2010 Census in particular, it seems that in most circumstances residents of the attached assisted living facility would be classified as “households” in the Census data, while the nursing home residents would be classified as living in “institutional groups quarters”. Here is a quote from this document (page B-8):
Housing for the Older Population—Housing specifically for the older population has become more and more prevalent and is being identified by many different names. Living quarters in these facilities— unless they meet the definition of skilled nursing facilities—are housing units, with each resident’s living quarters considered a separate housing unit if it meets the housing unit definition of direct access. These residential facilities may be referred to as senior apartments, active adult communities, congregate care, continuing care retirement communities, independent living, board and care, or assisted living. People may have to meet certain criteria to be able to live in these facilities, but once accepted as residents, they have unrestricted access to and from their units to the outside.
Housing units and group quarters may coexist under the same entity or organization, and in some situations actually share the same structure. An assisted living facility complex may have a skilled nursing floor or wing that meets the definition of a nursing facility and is, therefore, a group quarters, while the rest of the living quarters in the facility are considered to be housing units. Congregate care facilities and continuing care retirement communities often consist of several different types of living quarters, with varying services and levels of care. Some of the living quarters in these facilities and communities are considered to be housing units and some are considered to be group quarters, depending on which definition they meet.
Definitions of households and nursing facilities are given earlier in the document.