The button on the AutoUpdate toolbar allows you to set AutoUpdate ON or OFF. This is a global setting in the project, so any analysis that is set to auto update will first check the property of this button. It acts as an ON/OFF toggle. If ON, which is the default setting, then auto update will proceed according to the Recalculate Mode settings; however, if OFF then even if a Recalculate Mode is set to Auto for a particular analysis auto update will not occur until this global auto update is turned back ON.
This Auto Update ON/OFF property is useful in projects where you have many operations set to auto update and you want to control when the update occurs for all.