While it is true that sometimes grief can turn into depression, grief and depression are separate conditions.
The above mentioned conditions can also have similar symptoms which can easily be confused with each other.
There are many types of grief and each person experiences grief differently. Sometimes grief triggers depression, which is called a depressive disorder or clinical depression.
However, in some cases, grief is prolonged and may manifest as depression. In some cases, grief can cause depression.
In most cases grief manifests as symptoms of depression. In other words, what is called depression for some people is not actually sadness, but their sadness is manifesting as depression.