Many, if not all, components in a distributed system work independently, in parallel, with little interaction. For the most part, many of the systems in a distributed system work autonomously only communicating with a small collection of other components at interaction points.
An application written for a distributed computing environment may have many concurrent threads of operations.
Computers in a highly parallel machine are similar but not the same as computers in a distributed system. The computers in a highly parallel machine are much closer coordinated than the computers in a distributed system. The computers in a parallel machine share the same clock and memory structure, are typically managed by the same operating system, and typically, but not in general, share the same algorithm. Conversely computers in a distributed system don't share the same clock, don't usually have a common memory structure, and defiantly, aren't running the same operating system nor algorithm.
In some aspects highly parallel machines are similar to distributed systems. However, a highly parallel machine is not a canonical example of a distributed system.