Why does the word "adoption" describe a couple taking in a child AND describes child whose last name is legally changed to parent's spouse's?

When a child is adopted, he/she typically ends up living with a man and/or woman who the child doesn't know at first. But when a child's mother or father gets married, the child still lives with said parent. The only thing that changes is that the spouse moves in and becomes another legal guardian whose... show more When a child is adopted, he/she typically ends up living with a man and/or woman who the child doesn't know at first. But when a child's mother or father gets married, the child still lives with said parent. The only thing that changes is that the spouse moves in and becomes another legal guardian whose last name is now the child's. Exactly how does that count as adoption, if the child is still living at the same residence with biological parent while his/her spouse is the one moving in? When I hear the word "adoption," I think of abandoned children who need a home, not children whose last names were legally changed because their mom or dad got married.
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