A Doubt about a time convolution master equation

The same equation in 2 different books is different
I study of interaction between a system with a reservoir considering a weak coupling between them. I consider a bosonic bath, the initial state are separable and the operator of interaction between the system and bath is linear in the displacements of the oscillators.

In the book "Quantum Effect in Biology, Mohseni" , show that the time convolution master equation is:

$$\dfrac{d}{dt}\rho_{s,I}(t)=-\int_{0}^{t}d\tau Tr_{B}[\cal{L}_{SB,I}(t)\cal{L}_{sB,I}(\tau)\rho_{B}(0)]\rho_{S,I}(\tau)$$
where $$\cal{L}_{SB,I}(t) \hat{A}=\dfrac{1}{\hbar}[H_{I}(t),\hat{A}]$$ and $$H_I$$ is the hamiltonian system in the interaction picture.

but in "The Theory of Open Quantum Systems, Breuer" show that the time convolution master equation is:

$$\dfrac{d}{dt}\rho_{s,I}(t)=-\int_{0}^{t}d\tau Tr_{B}[\cal{L}_{SB,I}(t)\cal{L}_{sB,I}(\tau)\rho_{S,I}(\tau)\otimes \rho_{B}(0)]$$

I think that bot equation are not equivalent?

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