edit_page or edit-pages for current_user_can()?

You can find list of capabilities here:
Roles and Capabilities

There is no capability called edit_post nor edit_page. But…

There is also something called Meta Capabilities.

The capabilities listed on the Capabilities list are global capabilities. So they’re saying that user can edit posts or pages. But it doesn’t mean that given user can edit given post (for example editors can edit only own posts). This is where meta capabilities are used.