It's not about atomicity.

Co-Array Fortran is for multiple copies of the same program running on different data -- SPMD. Think MPI but much easier to write for.

You start a CAF program with mpirun. Multiple copies on the same machine or multiple machines in a cluster, your choice.

Embedded directives to process arrays concurrently is a different topic, and confusingly called OpenMP with no "I". Thus your multi-core CPU can process a numeric code more quickly.

You start a program using OpenMPI with it's own name --- ./a.out for example. You can control the number of threads used. Etc.