Trapdoors of Lattices: SampleD and SamplePre
No, they aren't the same. One of them maps 4 values to a single value, the other maps 2 values to a single value.

But yes, both functions have some similarities. Both compute the inverse of a known function witch can be computed only because a trapdoor is given (t in SamplePre and R in SampleD). We can use SampleD to create different SamplePre functions changing the parameters creating this way different trapdoor schemes.