Many times a house manager is there when kids are at school, so they can do more managing of the household just like a SAHM would do. They would make sure all items are in the house (toiletries, cleaning supplies, groceries), help with errands or cooking or tidying - it could be a variety of things. Usually caregiving is a secondary part of the job or would require some drop off and pick up of more independent kids.

House manager is like a stay at home mom. They do everything from shopping to scheduling repairs to driving kids to paying bills to hiring staff. EVERYTHING.

A house manager also pays bills, vendors, and takes care of all things related to the home, including staff, and outside contractors. Can also be expected to do personal assistant type stuff running errands, shopping, driving. These are usually high pay live-in jobs that require a mature person with years of experience working in a multi-staffed home.

The house manager needs a house staff to manage.
A nanny just needs a kid to nanny.
Or parents who still want to be nannied.

Between a nanny and a house manager?