Why is bleaching with chlorine permanent but with sulphur dioxide temporary? I was reading the properties of chlorine when I came across this statement:

Chlorine is a powerful bleaching agent; bleaching action is due to oxidation. Chlorine bleaches vegetable or organic matter in the presence of moisture. Bleaching effect of chlorine is permanent. $$ \ce { Cl_2 +H_2O -&gt; 2HCl + O} $$ $$ \ce { Colored Substance + O -&gt; Colorless Substance } $$

I searched it up and found out that bleaching with $\ce{Cl2}$ is an oxidation and is made powerful with the help of the nascent oxygen, hence it is permanent, but bleaching with $\ce{SO2}$ is a reduction and hence it is temporary.
Could someone please help me understand why the oxidation is permanent and the reduction is not? Is it powerful to an extent of the reaction not being able to get reversed? If yes/no, is there any quantitative/qualitative measure for the same?
The bleaching action of Chlorine is permanent because it involves the process of oxidation. $\ce{Cl2}$ reacts with water to produce nascent oxygen which combines with the material in question (by oxidising it, as pointed out by @Mathew Mahindaratne
) and makes it colourless.
The bleaching action of $\ce{SO2}$ is temporary because it involves the process of reduction. $\ce{SO2}$ removes oxygen from the coloured substance to make it colourless. Atmospheric oxygen slowly takes place of the removed oxygen, because of which the material regains it's colour.