Grief is a natural emotional suffering one feels with the loss of something.  Everyone grieves differently and this can depend on personality, coping styles, life experiences, faith, and nature of the loss.  Grieving takes time and there is no normal time period.  Common symptoms can include: shock and disbelief, sadness, guilt, anger, fear and physical symptoms.  In depression the feelings of emptiness and despair occur constantly.  One begins to see the other symptoms described on the symptoms page.  Once someone recognizes that it is depression and not grief, one must seek medicial attention. 
Dementia can have depressive symptoms and depression can imitate dementia.  In the beginning stages of dementia, when one realizes they are losing their memory it can lead to depression.  See chart on another website to determine the deference between depression and dementia.