The story “Two Kinds” by Amy Tan tells about the childhood of the protagonist, a Chinese-American teenager and the consequences of her mother's high expectations of being a child prodigy.
Possible interpretations of the title "Two Kinds" is mentioned by the narrator's mother: Only two kinds of daughters,… those who are obedient and those who follow their own minds….
Also, the narrator mentions two types of music, "Pleading Child" and "Perfectly Contented" and concludes, “… they were two halves of the same song”.
Here is the link to the text of the story:
https://s3.amazonaws.com/scschoolfiles/400/two_kinds_by_amy_tan.pdf