Both are a contract marriage story in which the two unexpectedly have a past connection. Both pairings have great chemistry. The same actor is the ML of DTMY and the SML of TTFIL.

Both have main characters who are cat/humans and end up living with a human.
...............................................................

FL is a cutesy cat/human living with a serious human ML.
.............................................................................

ML vs. FL is a cat/human who ends up living with the human ML.
.......................................................

Cat/human main character cohabitating with human.
...............................................................

Both have a strong FL who disguises herself as male and a military ML who learns her secret early on but hides it for her.

Both MLs are wealthy CEOs who have a traumatic past and issues as a result who end up cohabitating with the poorer FL. They later find out they met in childhood.

Both have a FL in a entertainment/fashion industry (makeup and livestreaming vs. singer and later clothing designer). MLs are cold at first then very doting when they fall on love. The secondary couples are very similar in both shows with a softer male who chases her vs. colder more distant female who pushes him away at first.

Both MLs are wealthy CEOs who have traumatic pasts and issues as a result. They hire FL (as a contract wife vs. bodyguard) and begin to heal as well as fall in love. There is a past connection between the two.

Poorer FL/rich ML. FL enters into some sort of contract relationship with the ML or his family for both their good, with no intention of falling in love. Both are romantic, tropey, and very enjoyable dramas.

Contract marriage to genuine love. ML falls and chases FL first. ML has a traumatic past, is controlling, and seems cold at first. ML and FL have a past connection that the ML remembers and the FL doesn't know until much later. There is a scheming SML who gets close to the FL in order to hurt the ML.

Both are contract marriages intended to only last a short time that turn into genuine love. One is historical, the other modern day, though.