Plot for the 1st one is that FL is the daughter of the emperor but it is revealed that she is actually the daughter of the late Queen's maid and was swapped w/ the OG daughter cuz the maid was jealous and because of that she is executed by her tyrannical father
2nd one is similar but FL is the daughter of a noble and the mother finds out early that FL is not her real daughter and so she neglects and abuses FL for it and then they find the real daughter
Plot for the 1st one is that FL is the daughter of the emperor but it is revealed that she is actually the daughter of the late Queen's maid and was swapped w/ the OG daughter cuz the maid was jealous and because of that she is executed by her tyrannical father
2nd one is similar but FL is the daughter of a noble and the mother finds out early that FL is not her real daughter and so she neglects and abuses FL for it and then they find the real daughter