It appears that what the author means here by a mistaken assumption is a mistaken assumption in belief, since he says, “and an invalid marriage.”
An example of a mistaken assumption in belief is where a man divorces his wife three times, and while she is asleep, another man comes to her, thinking that she is his own wife, and has intercourse with her. Does she thereby become lawful to the first husband? She does not, because this intercourse took place without a marriage.
His statement, “or ownership of a slave woman,” means that if the first husband’s wife were a slave woman and he divorced her three times, and her waiting period ended, she would be lawful to her master, because he owns her. Her marriage does not transfer ownership of her. Thus, if her master has intercourse with her by virtue of ownership, and she undergoes the required waiting period to establish that she is not pregnant—or she bears him a child and he then leaves her—does she become lawful to her first husband, who divorced her three times? She does not become lawful to the first husband, because she has not married. Allah says: “until she has married another husband,” whereas this woman has not married a husband.
His statement, “and an invalid marriage,” refers to a marriage in which one of the conditions of validity is lacking, or one of the impediments to validity is present. But is this the same as a void marriage, or is it something else? It is something else. The difference between them is that a void marriage is one whose invalidity is agreed upon by the scholars, whereas an invalid marriage is one concerning whose invalidity the scholars differ.
In the Hanbali school, there is no difference between an invalid and a void act except in only two chapters: marriage and Hajj. In these two, they distinguish between the invalid and the void. They say that a void Hajj is one in which something that nullifies it occurs, such as apostasy. Thus, if someone apostatizes during Hajj—may Allah protect us—his Hajj is void. An invalid Hajj is one in which he has intercourse before the first stage of release from consecration. As for marriage, the invalid one is that concerning which the scholars differ, while the void one is that whose invalidity is unanimously agreed upon by the scholars.