Command is an often used name that's used for very different functions. For example "Engine 2 to command." Who is he calling, dispatch or the incident commander? In most cases, he's calling the incident commander, not the dispatch center. An incident command is often set up for fires, major wrecks, and almost anything where there's a large response required. I've seen them used for firework displays and festivals even.
This name change was probably done to eliminate confustion on these types of situations where there's also a local incident command setup. It should also make things easier for mutual aid situations.
"XXX Command" is an Incident Command System ("ICS") term (where "XXX" is a name for the incident). Among other things, ICS is now widely employed for Fire Department incidents and some extended police incidents.
"Comm Center" could be a synonym for "Dispatch" (sometimes a/k/a "Control"), but it also could be used to signify an incident on-scene mobile comm unit, which is usually a function under "Logistics" in the ICS system. Technically, the primary function of the Comm Unit is to monitor all communications (in a repeated system, on both the input and output frequencies) to be sure that all messages are acknowledged and nothing gets lost. Secondary functions involve deploying replacement batteries, portables and the like as needed during the incident, perhaps maintaining either a comm log or an accountability log.
For a simplified overview of the ICS system, see
Incident Command System - Wikipedia, the free encyclopedia
The term "control" as a moniker for "dispatch," "base", or "fire alarm" seems to have started in the 1970s with the major shift to UHF, and appears to have been born by the reference to "Primary Control Point" in the revised form of FCC Part 90 license.