This is from my notes from my classes..
AOP - Two or more persons joining in a common purpose or action voluntarily for common objective. In an AOP, firm, Co., individuals can be members.
Example - Trust
BOI - It is formed by operation of law. It consists of only individuals. No common will or desire.
When a person dies without having will, and the property of such person falls in the hands of legal heirs then unless they enter into a mutual agreement or family arrangement, tax on income from such property shall be recovered from these legal heirs as a group. Such type of entity shall be BOI.
Example - On the death of an individual, a BOI is formed by operation of law, and the property of the deceased is of that BOI till it is divided between the members.