"shared" uses multiple processes on a single computer for the various coarray images. "distributed" uses multiple computers connected in a "cluster", one image per computer. The advantage of "shared" is that it has minimal setup requirements and can work well on a multicore system as long as you don't "oversubscribe" the cores. The disadvantage of "shared' is that there's a low upper limit on the number of images that are reasonable. With "distributed" you can have, potentially, thousands of images across thousands of nodes, but configuring this is not simple and the startup time is even longer than for "shared".
Coarrays do not use a shared memory pool. Each image has its own "piece" of a coarray and MPI (in Intel's implementation) is used to send data and synchronization back and forth.
