mourning vs grieving

mourning is a noun but grieving is not a noun.

Word	Noun	Adjective	Verb	Adverb
mourning	Yes	Yes	No	No
grieving	No	Yes	No	No

As adjectives, mourning and grieving are synonyms defined as:

Other synonyms of mourning include bereaved, bereft, grief-stricken, sorrowing.

mourning (noun)	grieving (noun)
the passionate and demonstrative activity of expressing grief
state of sorrow over the death or departure of a loved one

mourning (adjective)	grieving (adjective)
sorrowful through loss or deprivation	sorrowful through loss or deprivation