In a sense, the main difference between psychoanalytic and feminist readings of Charlotte Perkins's story "The Yellow Wallpaper" lies in where critics place the blame for the narrator's descent into madness, with psychoanalytic critics exploring the pysche of the narrator or Gilman herself as the source of the problems and feminist critics blaming patriarchal society.
Psychoanalytic criticism, either in its traditional Freudian incarnation or the more recent Lacanian structuralist and post-structuralist variants, has as a central concept that the most important elements of personality and what most strongly motivates people is not what is foregrounded in their conscious adult minds, but the subconscious desires and reactions formed in their early childhood and subsequently repressed. Thus a psychoanalytic approach to "The Yellow Wallpaper" would look at the story for hidden or repressed features of the narrator's psyche that cause unresolvable conflicts. For example, her reaction to her child and husband might be read as some form of transference of her mother's own rejection of her, or a surfacing of an Electra complex, in which her sexual attraction to her own father in her childhood leads her to feel conflicted about her love for her husband as her husband himself becomes identified with the role of father.
Feminist criticism addresses gender roles, and in particular the operation of patriarchy and its effect on women. Thus a feminist critic might see the enforced rest cure and the narrator's madness as the results of patriarchal repression, which traps women in conventionally domestic gender roles just as the woman herself is trapped in the room. Rather than looking for hidden causes of the narrator's mental state, a feminist would see the medical establishment as complicit in the oppression of women and an intolerable situation causing the disintegration of the narrator's mind.