Home care is a broad term that encompasses any service aimed at helping someone with health issues stay at home and out of the hospital. Private home care—or private duty home care—often refers to home care services that, while performed by a CNA (Certified Nursing Assistant) or HHA (Home Health Aide), are not strictly medical in nature. HouseWorks provides numerous home health care services aimed at helping seniors 'age in place.'
This may include of a number of supports: 

Personal care (dressing, bathing, general help with morning routines)

Medication reminders and assistance

Cooking, cleaning, or helping with laundry

Supplemental support for end-of-life care or hospice 

Escorted transportation

Dementia-specific support (companionship, redirection, providing structure, and activities)