The fundamental difference between a report & a dashboard is that you can apply filters to an entire report while you cannot filter an entire dashboard.
A report allows you to apply overall filters which limits the filtering options based on the common fields in the datasets used. Reports are also interactive. You can click on any chart in a report and it will update all other charts relative to the element you clicked. This is the same as using the normal 'add filter' option - just fancier!
A dashboard is a collection of reports. Every gadget on a dashboard is self contained and has a different underlying dataset.
As a result, you cannot apply filters to a dashboard as a whole. Instead, each gadget needs to be filtered individually. Equally, clicking on a dashboard gadget will not update the surrounding gadgets.