Important Updates informs you when a background upgrade of the listed components takes place. These can be controlled using the command-line softwareupdate utility and App Store preference settings in Systems Preferences.
Critical Updates refreshes your Components table upon launch. If it is left running, it polls the App Store to check for security updates. It also polls the App Store about once every 10 second while it is running. Critical Updates is very energy- and resource-efficient and can be left running without any impact on system resources.