The big difference between Sherlock being a private detective rather than a police detective is that he does not have to abide by a strict honor code. This means he chooses how to handle the outcome of the case, which doesn't always involve a call to the police.
The classic look of Sherlock Holmes: deerstalker hat, a magnifying glass, a pipe, a long overcoat, and the absorption into figuring out a case.
In The Boscombe Valley Mystery, a man has been murdered and his son is accused of killing him. Sherlock figures out who the actual killer is, John Turner, a dying old man who was blackmailed by the deceased for robbing a carriage of gold. Once Sherlock is done with the adrenaline rush from the case and figuring out who committed the act, he has to decide what to do with the man that has already confessed to him.
He decides, "I will keep your confession, and, if McCarthy is condemned, I shall be forced to use it. If not, it shall never be seen by the mortal eye; and your secret, whether you be alive or dead, shall be safe with us" (67). Sure, if a person was in the same shoes as Sherlock, they would see the cons of having this dying old man spend his last days behind bars away from the comfort of family and friends. The old man killed the guy because he didn't want the blackmail to continue to his next of kin, Sherlock could tell that he was not going to kill anyone again. There is the side of justice in the point of view of the law, the thought of why should this man who murdered someone gets to go free and is it really fair to the deceased that this happened.
He decides, "I will keep your confession, and, if McCarthy is condemned, I shall be forced to use it. If not, it shall never be seen by the mortal eye; and your secret, whether you be alive or dead, shall be safe with us" (67). Sure, if a person was in the same shoes as Sherlock, they would see the cons of having this dying old man spend his last days behind bars away from the comfort of family and friends. The old man killed the guy because he didn't want the blackmail to continue to his next of kin, Sherlock could tell that he was not going to kill anyone again. There is the side of justice in the point of view of the law, the thought of why should this man who murdered someone gets to go free and is it really fair to the deceased that this happened.
The man who committed the murder died several months after his confession to Sherlock and the son of the deceased was acquitted. So no one really got the blame for killing Charles McCarthy, and everyone had a happy ever after except Charles McCarthy.