It might be a little unclear for what we actually do then. As a designer we focus on gameplay, technical brushwork (clipping / portalling / mantles / etc), cover placement, flow, and game logic like spawns.
Once a map gets to the technical brushwork level where I'm mostly doing portalling or clipping the artist's work, I start a new level and keep flexing that level building muscle. I've got a pile of ideas I'm ready to roll on, just incubating them until its their turn.
Art handles the detailing of the level and the art direction. I tend to detail a little more than the other designers because its just what I'm used to, but its not uncommon to see levels dev (or case, as the textures are called in COD) textured going into art after being design locked. If I think an idea is really working I'll put an extra day into an area to really sell it. I don't make any custom assets save for the loading screen and the compass map.