We typically refer to the rest as an extended family, but I guess you could call my concern as one for having an immediate family. Of course, different cultures have different ideas about all of this (I’m specifically biased by growing up in an American nuclear family unit far away from extended family connections with no help during financial difficulties).

I’m an American and I sure as hell don’t refer to my parents as my “extended family” even though I’m married with children.

Neither do I, even if they aren’t around anymore, but that is hardly the point grand parent was making.

No, they were referring to the difference between having to support yourself versus the responsibility towards having to support your family. This could be their grandmother. It could be their children. It could be their pack of dogs. It doesn't matter, the point is singular vs multiple responsibilities of basic necessities.