Answer
In a Galilean transformation: $$ x’=x-V_x t,\qquad y’=y-V_yt\, ,\qquad z’=z-V_z t\, ,\qquad t’=t $$ whereas in (spatial) translation $$ x’=x-r_x\, ,\qquad y’=y-r_y\, ,\qquad z’=z-r_z\, ,\qquad t’=t\, . $$ The Galilean transformation depends explicitly on the relative velocity $\vec V$ and the time $t$: for different $t$’s you add a different vector $\vec V t$, whereas the simple translation adds a fixed time-independent vector $\vec r$ to each coordinate.
Since the bit you add in the Galilean transformation is time-dependent, it affects how velocities transform: $$ \vec v’=\vec v-\vec V $$ whereas, for a simple translation, $\vec v’=\vec v$ since there is no time-dependence on the shift in position.
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