gun rights and mental health

According to ncsl.org, in the state of Alabama, "No person of unsound mind shall own a firearm or have one in his or her possession or under his or her control." When I read this, it raised some questions. There are many mental illnesses, do all mental illnesses prohibit someone from owning a firearm, or are there certain ones? Are mild mental illnesses included in this? I learned from Law Center that "Federal law prohibits firearm possession by individuals who have been 'committed to a mental institution' or 'adjudicated as a mental defective.' This prohibition however, does not include many other individuals known to be dangerously mentally ill." So, only severely mentally ill people cannot own guns, and from this source means only people who have been put in a mental institution or have been diagnosed with some sort of sever metal disease. This could be a problem in my opinion, because there are a lot of people who have mental illnesses but haven't been diagnosed or are even aware of the issue. These kinds of people would be able to buy a gun, which is still very dangerous, but the prohibition of diagnosed mentally ill people from buying firearms decreases the probability of a mass shooting of some sort.