This is a bit of a simplification, but should help explain:
If you want to tell something to change (turn a light on, change the thermostat to a new temperature, start raising the blinds, etc.), then you want to send a command to an item. If your items’ states are not being updated by a binding, the autoupdate feature (see below) or something else external, you will probably want to update the state in a rule, using postUpdate.
When you click on buttons, sliders or other widgets in the UI, that sends commands to items. Usually this causes the state of the item to update automatically at the same time (using the default autoupdate feature), but there are causes where autoupdate is not performed, depending on the binding or configuration in your .items file if autoupdate="false" is present. Commands can also be sent other ways, such as the REST API and CMD servlet.
Your rules can trigger on items receiving commands, items’ states updating, or items’ states changing to a different value.