I think you should share the diffractograms.

So we could better see what you mean by 'two powder xrd pattern are the same' and whether they are really the same (from the XRD point of view).

Thanks in advance

I agree with Dr. Martens.

I think the XRD data of them will show some difference. No two materials/compounds have the perfectly same patterns, it may looks same but anyway it will slightly differ. 

When two compounds have similar XRD patterns (not the same) that mean they may have the same crystalline structure. But with analyzing these patterns you can find many differences.

thanks

As you mentioned the core of your materials are the same. So are the same XRD patterns deried from the core or your modification layer? Based on my experience, weak diffractions derived from thin coating layers are likely to be ignored considering the diffractions of the body materials are strong. Besides, melting point is not a precise way to identify compounds. Melting point can be varied with the partical size, Eg. silver nanowire melts at lower temperature than the large blocks. You can also use Transmission electron microscope(TEM) to study the latice frings and conpare the  interplanar spacing with the that of a particular phase, which is a more convincing characterization.

You may also consider that a small amount of amorphous phase won't show on an XRD pattern, but may influence the thermal behaviour.

We need to check the peak positions exactly even then if they have same positions  then both are same material. But they may be exist in different morphology. 

Identical XRD patterns are a quite strong indication that the two materials are the same, at least if you are working with a pure single phase. However, you need to look at the XRD patterns very carefully, as small changes in peaks exact position, or small extra peaks can indicate that the two materials are not the same. For example, a shift in the peaks may indicate the presence of doping, while even very small secondary peaks often indicate the presence of impurities, which affect the thermal behavior.

Before concluding that the two material are the same I'd strongly suggest to compare them using another "local" analysis technique. Indeed, XRD being a bulk technique, may not show inhomogeneities, small amounts of secondary phases... As already suggested, the best complementary technique for me is TEM with diffraction patterns and EDX, but also EDS-SEM or Raman spectroscopy, for example, could be useful.