In Galelian transormation we assume that we are in non-relativistic domain, So there so time dialation nor length contraction, in two reference frames which are having a uniform relative velocity with respect to each other, since this velocity is much less than C,the velocity of light.
Lorentz transformation is applied when the uniform relative velocity between two frames is comparable to C and hence both time dilation and length contraction both come into play in the trnsformation.
If we assume Frame 2 has uniform Velocity U along X-axis with reference to Frame 1
In Galelian Transformation : U<<C ; X = X'+Ut , Y = Y' , Z=Z'
In Lorentz transformation: U comparable to C ; X = X' +Ut Sqrt(1-v^2/c^2) , Y =Y' , Z= Z'
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