The main difference between the narratives of "Two Kinds" by Amy Tan and "A Red Dress" by Alice Munro is that the protagonist/narrator of Munro's story appears to fulfill her mother's expectations, while that of Tan's story cannot, at least, not during the mother's lifetime.
There is also the difference in the fact that Jing-Mei's mother sets unattainable goals for her daughter while the narrator's mother in Munro's story only expresses her wishes for her daughter's happiness through her actions of making the fancy red dress and then using the lingo of her daughter and her friend when they depart for the dance. Certainly, underlying each narrative is the common desire of mothers to somehow vindicate themselves through their daughters, by wanting to share in their daughters' successes because doing so will give them a sense of fulfillment that they lack. For instance, in "A Red Dress," after being walked home by a boy, the daughter narrates,
But when I saw the waiting kitchen, and my mother in her faded, fuzzy Paisley kimono, with her sleepy but doggedly expectant face, I understood what a mysterious and oppressive obligation I had to be happy....
In "Two Kinds" after Jing-Mei fails, she notices the sense of failure that her mother experiences, as well:
But my mother's expression was what devastated me: a quiet, blank look that said she had lost everything.
Another difference that exists is in the distance that grows between the mothers and the daughters. In "Two Kinds," Jing-Lei has given up on the piano and asserts her right to fail:
In the years that followed, I failed her many times, each time asserting my will, my right to fall short of expectations.
However, the daughter in "A Red Dress" vows to not let her mother know that she has not always succeeded in relationships.
I understood what a mysterious and oppressive obligation I had to be happy, and how I had almost failed it, and would be likely to fail it, every time, and she would not know.