Yeah I was drunk. I meant Swan Lake.
You could look at Swan Lake literally and conclude that it is about a half woman /half swan, full stop. Like you said Black Swan is about ballet, full stop. But really there are mutual themes in both narratives. As a couple of people have said the film mirrors the ballet. What is common to both narratives is the transformation of a young woman into adulthood, more or less.
She literally goes from living the life of a child to being a confident, sexually liberated woman. It's black and white. There's her world with the childlike room and stuffed toys (as Raz said), the overbearing mother that treats her like she's a little girl, her exaggerated naivety, etc. and then there's the adult world with it's blunt sexual comments (instructor man telling her to masturbate, asking her if she likes sex), the sexually uninhibited temptress character, the drugs, etc.
Honestly I'd say that the broader themes of the film are more significant than the context (ballet). You could tell the same story about all sorts of different performance artists or, as it was originally told, about a poultry princess. Although the film is clearly some sort of homage to the world of ballet, the core of the story is not ballet.
Yeah they share the same question but are still very different films. L2R said he thought they were both character studies. I disagree. While both films focus heavily on their protagonist, Swan is driven by tension/madness rather than character depth/development. The Wrestler is purely character-driven drama. Black Swan is an ultra-stylish Thriller/Horror/Mystery with emphasis on special effects and cinematography.