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An oxidation state is an Electron-bookkeeping assignment to a chemical atom: its electric charge number after the ionic approximation of bonds. It helps identify oxidation and reduction and determine stoichiometry, even for covalent bonds without separate charged ions. In water, each hydrogen has oxidation state $+1$ and oxygen has $-2$; this does not assert that a water molecule contains two free protons and a free oxide ion.^[ref]

Three conventions answer different questions. Formal charge divides each bonding electron pair equally in a chosen Lewis structure. Oxidation state uses the ionic approximation of bonds. Partial atomic charge instead partitions the actual electron density and depends on that partition. In the ordinary water Lewis structure, every formal charge is zero although the oxidation states are not. Neither bookkeeping convention supplies numerical partial atomic charges.

A redox chemical reaction couples oxidation and reduction. In the electrode examples here, oxidation releases Electrons and reduction accepts them. ^[ref]

Redox can be recognized by changes in oxidation state: an increase records oxidation, a decrease reduction. These are formal Electron assignments, distinct from measured partial atomic charges. Half-reactions expose the matching loss and gain, making electric charge conservation visible.^[ref]

The Electron accounting need not describe free Electrons travelling between spatially separated chemical species. For example, in $2{\mathrm{H}}_2+{\mathrm{O}}_2⟶2{\mathrm{H}}_2\mathrm{O}$, hydrogen changes from oxidation state $0$ to $+1$ and oxygen from $0$ to $-2$. Four hydrogen chemical atoms lose four formally assigned Electrons in total; two oxygen chemical atoms gain four. The water product has covalent bonds, and these assignments do not turn it into separated ions. See ionic approximation of bonds and electron transfer and ionic character.

By contrast, neutralization can rearrange chemical bonds without changing oxidation states:Hydrogen remains $+1$ and oxygen remains $-2$. The aqueous proton notation abbreviates its interaction with water. This acid-base chemistry example conserves electric charge but has no matching increase and decrease of oxidation state; movement of ions or a change of chemical bonds alone does not establish redox.