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Basically they are very similar the only big difference is that formal charge assumes all the bonding electrons were divided equally between atoms while in oxidation numbers we assign numbers to the more electronegative atom in the bond.
For formal charge, you're assuming that the bond is fully covalent and attribute one electron to each atom. For oxidation number, you take into account which atom has the highest electronegativity and attribute the whole shared pair to that atom.
We can obtain oxidation numbers by arbitrarily assigning the electrons of each covalent bond to the more electronegative atom in the bond. This is in contrast to the Formal Charge which divides each bonding pair equally without concern for which atom may be more electronegative.
Oxidation numbers are found by assigning the electrons in the covalent bond to the more electronegative atom in the bond. The formal charge is different because the number isn't determined by which atom is more electronegative.
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