Hello Luca,
CCTK_ReductionArrayHandle is used in several thorns but it is not described in the ReferenceManual. Is it (still) supported? How is it different from CCTK_LocalArrayReductionHandle?
It's part of the "old" reduction interface. Which happens to be the one Carpet supports, so it is widely used :-). I doubt support will go away anytime soon. The calls are documented in the User manual in section C1.7.5 (page 84 in my build).
As for differences I'd consult this section and the reference manual. It seems that one is a reduction over local arrays (ie double a[100]) while the other reduces grid functions (or grid arrays or grid scalars most likely).
Yours, Roland