[FEA] Reduce duplication between C++ and C APIs

[cjnolet]

We have several C headers that are redefining enums and structs from the corresponding C++ files. This is quickly going to become a maintenance burden, and even worse it leaves us at risk of making updates to the C++ API constructs that don't propagate to the C constructs.

As an example, I consolitated the DistanceType enum into distance.h and simply import it into the C++ namespace in distance.hpp. We should do the same across all public APIs.