Love & The Emperor (2020)

Both are mostly light dramas with a similar feel. The FL is from another world and arrives in the historical/other one in the body of an "ugly" maid vs. "ugly" concubine. ML is royal in both.

In both the protagonists enter a game to live an adventure...............................................................

The two dramas are an inversion of each other - one is a real world person entering the world of a historical game, the other is a person from a historical game entering the real world.

Both dramas have a modern day FL in ancient times falling in love with the emperor. Both feature scenes of the two eating together.

Both are dramas about a real world FL who enters the world of a historical game/VR where they find true love.

- there is a romance in the game where they meet
(However, there is also romance outside the game)
- the focus is on the romance between the female lead and the male lead (mostly outside game)
- the male lead in Love 020 makes video games (much like her crush in Love & the Emperor)

In Love 020, more of the story takes place in present time, but it has the same sweetness between the characters. This is the drama series and there is also a movie version. The series can be found on viki.com: https://www.viki.com/tv/36373c-love-o2o

- the main leads meet in a game
- the focus is on their romance

This is a movie version, but there is also a drama series called "Love 020" which is longer. I personally prefer the film because of the two main leads. The movie can be found here:
https://www.youtube.com/watch?v=VLBqhQ2_rIE&list=PLzHjyNBiCpSEe1M0QhCzo-kIkENOngOkO&index=1&t=56s

ML is an emperor or the son of the emperor, and the FL is a plucky servant in the palace who wins his heart with her cooking. Both are sweet dramas.

Both dramas are about a modern day FL who enters a historically set game and must pass the levels to return to the real world.

- the female lead also enters a different world (not a game)
- the male lead falls for the female lead

In this drama series, the female lead enters a comic book/alternative reality to save the male lead. It is quite gripping and well-made. You can watch it on Netflix.

Both dramas are about real world leads who enter the world of a historical game which they must win to return home.