The definition of formal Charge
A good description appears in the book, "Chemistry A Molecular Approach". 

In the molecule of hydrogen fluoride, we know that it has a dipole moment, and fluoride is slightly negative. Ignoring this information (electronegativity difference) and we share the bonding electrons equally, the formal charge can be calculated, and both of them are determined to be 0.

In reality, we know that fluoride has the electron from the hydrogen most of the time (due to electronegativity difference). We say the hydrogen has a partial positive charge and the fluoride has a partial negative charge. 

From this, it is apparent that the formal charge is different from the charge on the atoms in a molecule.