Parallel programming on a cluster system with network connection most often uses MPI, but may use Intel Cluster OpenMP, or, possibly, something like Fortran 2008 co-arrays or UPC.  Parallel programming for a multi-core system most often uses threading, such as OpenMP or TBB.  Fortran, C, and C++ are in widespread use for both MPI and OpenMP programming, with large programs commonly using 2 of them.  "hybrid" combinations of MPI and OpenMP are becoming increasingly important.