The idea of having a stepbrother or having a half-brother comes when there's either divorce between two partners or due to the death of any of the parents. When this happens, there will be different suggestions for the woman or the man to marry another person. A half-brother is a male kid who has a different father, but the same mother, this is also known as a maternal half-brother. In other words, it refers to a male kid who has a different mother, but the same father.
This is known as a paternal half brother. A stepbrother, on the other hand, simply refers to the son of one's stepfather or stepmother who is not the son of one's mother and is not the son of one's father. Another difference is that a stepbrother is not related to one of the parents by blood, but a half-brother is not related to you by blood
A stepbrother is someone that becomes your brother as a result of your parent {father or mother} marrying someone else while half brother is your brother due to both of you having one common biological parent. A step-brother doesn't have any blood relationship with you but can only be related to you either by one or both of your parent that got married to another person either after a divorce, death or any reason that causes them to separate.
In other hands, half brother is entirely different from a stepbrother because half brothers are always related by blood. In most cases, you may not even know you have a stepbrother, but in case of a half brother, you will surely remember. Half brother is your real brother in accordance to the law, and he has access and right to your property while a half brother is not your real brother and have no right to your property according to the law.