In very broad terms:
cuda.hdefines the public host
functions and types for the CUDA
driver API.cuda_runtime_api.hdefines the public
host functions and types for the
CUDA runtime APIcuda_runtime.hdefines everythingcuda_runtime_api.hdoes, as well as built-in type
definitions and function overlays for the CUDA language extensions and
device intrinsic functions.
If you were writing host code to be compiled with the host compiler which includes API calls, you would include either cuda.h or cuda_runtime_api.h. If you needed other CUDA language built-ins, like types, and were using the runtime API and compiling with the host compiler, you would include cuda_runtime.h. If you are writing code which will be compiled using nvcc, it is all irrelevant, because nvcc takes care of inclusion of all the required headers automatically without programmer intervention.