As with many words in this area, they are used loosely. It helps if there are distinctions. It helps if you use plain English.
I use “scorecard” when I am looking at a table of figures with results on them. Its a set of scores on a card (hence scorecard).
I use “dashboard” when the presentation is much more graphical and especially when full of dials and sliders. The image of the report is more like the dashboard of a car or aircraft. Personally I am not keen on dashboards as they are often a triumph of presentation over content and information. Also vehicle dashboards tend to display what is happening now or current state, rather than what has been happening (eg how fuel consumption of speed varied). This “instant” view is not that helpful for a business. Unfortunately dashboard gets used a lot for any graphical performance report.
There is a richer report format that includes graphs of performance over time, (Rarely seen on a car dashboard) together with commentary, and actions that are being taken to resolve or address problems. This is much more a “performance report.” It is how good balanced scorecard reports are presented, but is not as simplistic as a simple scorecard.
I used ‘the scorecard part of a balanced scorecard’ when I am referring to a scorecard that has been built specifically with four perspectives, that have a cause and effect relationship, that have objectives and has been developed with a Strategy map.
I use Balanced Scorecard Approach, to refer to the whole way of using the thinking and whole methodology for the capture, communication, implementation and management of strategy