Yes, serial HDF5 and Parallel HDF5 (PHDF5) are part of the same HDF5 source code. Parallel HDF5 is a configure option that you can specify to build HDF5 with:

  ./configure --enable-parallel

HDF5 "knows" certain parallel compilers and will automatically enable Parallel HDF5 if one of those compilers is specified in the CC environment variable. See the parallel installation instructions in the source code for more details.