DCS is a bunch of computers and controllers hooked up together to control physical process. DCS is 1-vendor solution meaning all components, such as controllers, HMI, servers, engineering stations, applications are designed and produced by the same manufacturer and integrated into a single distributed  solution.

In contrast to PLC-based solutions, the components needed for process control (HMI, servers, applications) might be from the different vendors.

Controllers used in the DCS are typically called controllers and not PLCs. PLCs typically have all the needed control logic and do all the needed computations to run the process on their own. Controllers has some portion of logic and do some computations, but the biggest chunk of control logic is executed on the DCS server (which orchestrates works of other controllers).