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The rate of formation is specific to each product, while the unique rate of a reaction is the same value for all reactants and products in the unique reaction.
The rate of formation is simply the rate of formation of a given product (or rate of consumption for a reactant). This is the value you get when you take the change in concentration over change in time, or d[R]/dt for the instantaneous rate. The unique rate of a reaction is when you take into account the stoichiometric coefficients to determine the unique rate that is the same for all reactants and products in that "unique" reaction.
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