Both are mini dramas in which the ML enters into a contract relationship with the FL with her pretending to be his long lost sister in order to comfort a sick relative (father vs. grandfather). The two then fall in love.
FL has a contract relationship with the ML (pretending to be his sister vs. being his wife for a short while) which is to benefit the ML's father in some way. Both are mini dramas.
Both are mini dramas in which the ML and FL agree to a contract relationship as relatives (brother and sister vs. father and daughter) for the ML's need to please a relative, and while living together they fall in love.
Both are mini dramas in which the rich ML is in a contract relationship with the FL to pretend to be someone else (his long lost sister vs. lost fiancée) in order to make his sick grandfather happy.
Both dramas involve the FL pretending to be someone she looks exactly alike which leads to the ML making her pose as that person. She then enters a wealthy family whose grandfather is ill.
One is modern and the other historical, but both have the same basic premise of the ML convincing the FL to pretend to be his long lost sister to make a grandparent happy. Along the way, the two fall in love.