He could feel the anger 'boiling up' inside him. [=he could feel himself becoming very angry]
The water in the pot is 'boiling over'. = The pot (of water) is 'boiling over'.
The kettle (of water) is 'boiling'. = The water in the kettle is 'boiling'.
(..) - You know what I mean. You can't tell me you're afraid of heights. I'm just a little uncomfortable about being on a rickety bridge over a boiling lake of lava! . For emotional support, we'll just tackle this thing together one little baby step at a time. - Really? (..)2001 Shrek