Similarities :
Mothers want to know the true
Child had a man made accident
Differents povs
Differences:
Confessions is darker, and gloomy
Confessions is leaning towards revenge

The wife also first suspects his husband has an affair, and she begins to investigate his colleagues

Both dramas have time travel and romance. In Ruk Laek Pop a man went to the past through a passbook. Both deal with a protagonist trying to adapt to the era's old customs.