CKEditor set its own CSS classes for text areas, but that would not explain why copying the CSS files from a theme to another doesn't change the visualized styles.
The problem here is that simply changing the files used by a theme doesn't change the used styles; you need to let Drupal know the theme has been changed, and this can be done in two ways:
- you select a different theme as default one, disable the theme you modified, re-enable it, and select it again as default theme
- you force Drupal to refresh the cache it is using, or you empty the cache tables
In the first case, you submit the theme selection form after each operations.