TL;DR: I guess the hash unique approach is technically a radix sort in base-64 if you hash the inputs before applying the radix sort, but a realistic radix sort will use far fewer buckets giving it much better cache locality and won't unnecessarily hash the buckets.
Also it's possible to write a radix sort that doesn't use any extra indirection, but that's a much more complex implementation and I doubt it really has any performance benefits.
