A dispatch console doesn't have to have CAD, if the dispatch center is using pen and paper to take, log, and dispatch calls. But if a dispatch center has a CAD system, chances are all of the dispatch consoles (workstations) will have a CAD terminal. The calltaker takes the 911 call and enters it into the CAD system. It then shows up in the pending queue of the dispatcher's CAD. The dispatcher then dispatches the call. They can give it out over the radio, send it to the appropriate unit(s) from the CAD to their MDC (if so equipped) or both. CAD will normally recommend the closest available unit(s) to send to the call, based on parameters set when the system is installed.
In the dark days B.C. (Before CAD), we would write everything down, look up the addresses and streets in a big book (if we didn't already know where they were), and send the units via radio. I can still hear the "ker-chunk" of the time clock as we stamped the time received and time dispatched on the starter cards. Whenever CAD went down and we had to revert to paper starter cards, my muscle memory caused me to grab the starter and push it to the spot where the time clock used to be, waiting for the "ker-chunk". We had to know the address and district of every bar, every apartment complex, and every trailer park. CAD ends up becoming a crutch if you let it; then when you're without it, you have trouble remembering any of that. Newbie: "Why do I have to learn that when CAD does it for me?" Me: "'Cuz CAD ain't always there..."