It is categorically different. If your memories of 1000 years ago gradually fade away, only that old version of you is "gone" (in present experiential sense).

It is categorically different. If your memories of 1000 years ago gradually fade away, only that old version of you is "gone" (in present experiential sense). You and your family and friends have known you as a consistent "self" with mental continuity throughout your whole lifetime. When you die in the current times, you and your family grieve and experience suffering as a result of the lack of your mental continuity. When parts of you later end up in a tree or squirrel, that is not a particularly consoling idea to those who would prefer you continued to exist as a human.