The rate law of Cannizzaro reaction in mild base is
$$\mathrm{rate_1} = k[\ce{RCHO}]^2 [\ce{OH^-}],\tag{1}$$
while in concentrated base the rate becomes
$$\mathrm{rate_2} = k[\ce{RCHO}]^2[\ce{OH^-}]^2\tag{2}$$
according to most sources I've read. But in both cases in the RDS hydride shift there is no base molecule among reactants. It's just the anion or dianion of the hydrate and the aldehyde reacting. So, why does the rate law include a base term?