@Le_Flemard If your father remarries a woman, she is your step-mother. When you get married, your spouse's mother is your mother-in-law. I think whatever term is used for it in some languages simply doesn't translate well, so it gets like that when tler's are lazy, lack reading comprehension, or use mtl. Sometimes it's also because english isn't their first language.
Also, I think it gets tl'ed as mother-in-law even when it is an adoption. Your stepmother or adoptive mother would be your "legal or lawful parent", so I think that's likely where the confusion is from.