I’m not an expert, but my understanding is that a family bank is often a combination of a family limited partnership and a trust that is designed to get money out of an estate. The bank usually makes loans to members of the family at reduced interest rates. The trust administers it and can decide whether or not to make the loans. On a smaller scale, one could simply designate an investment account as the “family bank” and use it in the same way, however the asset would still belong to the person whose social security number is on the account and thus they would be responsible for the taxes and it would be in their estate at death.
A family foundation suggests to me that it is intended to make charitable gifts – again a way of getting money out of an estate. The trust/foundation document would set the ground rules surrounding how, when, and to whom the gifts could be made.
Both vehicles give the wealthy grantor the ability to control the money after death by laying out the parameters in the trust and foundation documents of how and why the money can be used.