What is the difference between formula bar and name box?

The Formula Bar displays the current content of cells and allows you to add in formulas, labels or values into a cell. You can also start the Insert Function dialog box by clicking on the fx at the beginning of the formula bar.

The name box shows the address of the current cell selected or the name of that cell if a special name has been given to it. It can also show the name of a range. The name box appears to the left of the formula bar.