Parallels between My Devine Emissary and Wonderful Fate include:
The female lead is a student who is struggling academically and is reluctant to take her tests.
She travels back in time and/or into a historical narrative, where she encounters the ML, the emperor.
The connection between the leads in both dramas is that the leads characters are quite similar in that they initially despise one another before becoming friends.

My Debine Emissary is the Chinese version of Splash Splash Love.
It's a remarke version, from the outfit the female lead wore before travel to the setting, in episode one is the same.
Yes in the chinese version we can see a full on fall out between the mom and the daughter and we had a little flash back to see the father instead of just a picture

Both drama are the same expect there country oringin
One is Chinese (original) and the other is the Thai version of the original

Both shows explore the dynamics of age differences within couples, delving into their complex emotions towards each other. The storylines also consider the impact of external factors and the female lead's challenging history with past relationships. The age gap adds an additional layer of complexity, making it harder for the female lead to fully trust her spouse and open herself up to love. The shows also delve into the intriguing dynamics of age differences within the couples. Each performance skillfully highlights the couples' deep affection for each other, while also shedding light on the intriguing age gaps that exist between them. Both presentations thoroughly explore the emotional dynamics within each couple's relationship, regardless of their age differences.

Both of them were affected by a tragedy in the past that they felt wasn't properly justified, which is what drove them to take matters into their own hands.
They give off the impression that "if you want justice, you have to acquire it yourself."