Mourning is to commemorate and remember the lost life, or to express respect and sorrow for a certain person, a certain collective, a certain event, etc. It is a way of expressing emotion and respect, usually through some ritualized acts. For example, after the death of a person, people will express their condolences by lowering the flag at half-mast, silent mourning, bowing, etc., as a way to commemorate the deceased person and express respect and cherishment for life.
Mourning is a more profound and concrete way of expressing grief. It is usually an action taken to show compassion and support when an individual or group of people is experiencing misfortune or harm. Acts of mourning include not only ritualized behaviors, such as silence, bowing, etc., but also more substantive behaviors, such as donations, condolences, and help. The purpose of the condolences is to bring substantial help and support to the victims and their families, as well as to express sympathy and concern for the victims.
In conclusion, mourning is a more general way of expressing grief, and it can be an act in various forms; Mourning, on the other hand, is more specific and profound, and usually involves substantial support and assistance. Both are meant to pay homage to the lives lost and to show compassion and concern for the living.