Many legal documents use the phrase “my heirs and assigns.” There is a difference between those two categories of individuals.
My heirs are those individuals who legally will inherit my property if I leave no legal document (such as a will) giving that property to someone else. My assigns are individuals to whom I have assigned property via a legal document that I have signed.
If person A dies having only had one child (call them B) and that child survived him, then that child is his heir (will or not). B’s children are not person A’s heirs when A dies as long as B is alive. A could easily, via a legal document, assign or give their property to B’s children–making those grandchildren their “assigns.” B would still be the heir to whatever property had not been assigned.