The "grey bar" is the bezel. The older MacBook Pros and the older MacBook Airs had the all-silver physical bezel, one which was significantly thicker than the current black bezels on today's MacBook Airs and MacBook Pros.
How to enlarge the window and make it fill your screen:
How to Resize a Window on a Mac
- Move the pointer over the resize corner in the bottom-right corner of the window.
- Hold down the left mouse button and drag the mouse. The window grows or shrinks as you drag the mouse.
- Release the left mouse button when you're happy with the new size of the window.