Henrik Ibsen is considered the father of Modern Realistic Theatre. His writing style is concise, objective, and natural. He does not include allegorical symbolism in his work, nor does he add solliloqui, asides, nor inner thoughts to his characters. All his characters are well-rounded and typical of their social and economical sphere. He took the well-made play formula and integrated topics that are often considered controversial to include prostitution, venereal diseases, and the role of women in society.
Anton Chekov, contrastingly, is more into symbolism, psychological issues, and inner exploration. He also writes realistically, since his characters are often victims of their own fates. There is a hint of hope in tragic situations, and there is always an easy solution to the problem of the story.
What makes both writers similar is that they assign causes and effects, actions and consequences to their characters. There is no "miracle dust" that would come out of nowhere to get a character out of a scrape. Also, all their characters will suffer the consequences of whatever actions they choose to do.