Trapdoors of Lattices: SampleD and SamplePre In Trapdoors for Hard Lattices and New Cryptographic Constructions by Gentry et. al, they discuss SamplePre and in Trapdoors for Lattices: Simpler, Tighter, Faster, Smaller by Micciancio et.al, they discuss SampleD.

But still, I cannot understand whether the functionality id same or different. Can you explain?
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.