I was talking specifically about the PS4. I don't know why I thought they'd use OpenGL, I just naively thought Xbox == DirectX and PS4 == OpenGL. Seemed easier for the devs to port their games on a well known and documented API.
The PS4 uses a couple APIs for game graphics, GNM and GNMX[1]. I've heard that their shader language is similar to GLSL (corrected by lunixbochs). The menus are built in WebGL running inside a stripped-down Webkit browser. Developers are unable to use WebGL for games, but it isn't out of the question that will be supported in the future.
What do they use instead? A custom API?