I know death and all of the psychological aspects surrounding it are a very taboo topic, especially in America. We tend to have a high rate of death anxiety--feelings of apprehension surrounding anything to do with death to the point of attempting to avoid the topic all together. I recently wrapped up a course on human development, so it happens to be fresh on my mind.
Bereavement: a state of existence, such as being married or being single, that occurs when one has lost someone from one's life. Bereavement is not an emotion or a psychological state. It is simply what we call the time after a loss. The length of bereavement can technically be the rest of your life. However, it tends to have stronger social implications and limitations. Some cultures place an unwritten limit of one year. Some have longer periods, some shorter, in which a person suffering a loss through death is given sympathy and understanding.
Grief: the (sometimes intense) emotional and psychological response to a death. Many individuals experience profound sadness, shock, anger, apathy or indifference (usually as a defense mechanism, not necessarily because the person is callous), or a myriad of other emotional states upon experiencing a loss. The degree of grief felt is dependent upon many factors--the survivor's personality, the relationship with the deceased, age of the survivor, age of the deceased, cultural expectations, and many more considerations. Some people grieve quietly inside, some people make a huge show of "grief" even though they don't actually have any deep feelings for the deceased. When you "give someone grief" you are finding a way to make their life miserable, often attempting to heap guilt and sorrow into their hearts in order to lower their self esteem. Usually, this is a tactic of people who like to manipulate others to do their bidding. If you've ever experienced a "guilt trip," then you know how powerful (and scummy!) this practice can be, and how much damage it can cause.
Mourning: the formal process following a loss. Including funeral rites and body disposal rituals, mourning also encompasses the steps that a person takes in reconciling with the loss and continuing on with his/her life. When someone is in mourning, they are dealing with a death. They may be coming to terms with the reality of the loss. They may be handling the finances that surround death--medical costs, funeral costs, insurance paperwork, inheritance. They may be digging up old memories of the deceased and sharing them with others. They may or may not be experiencing some extreme emotional upheaval (grief), but they are in the process of coping with the death.
Death affects individual survivors differently. Understanding and patience are the greatest gifts we can give anyone during bereavement. However, it is probably not fair to the memory of the deceased to milk their death for all you can--using it as an excuse to garner sympathy from others or to skip out from school or work because you're feeling lazy. Ultimately life does continue on, though it sometimes takes us a while to get back on track. The key is to keep moving forward.