These are two terms that the BI world uses interchangably. The only thing they should have in common is that they both can visually display data.
Defined:
Scorecards are tools that help facilate discussions around strategy and operational performance management. The indicators (KPIs) should foster discussions about corporate direction, resource allocation, priorities, and initiatives.
Dashboards should be used for tactical discussion triggers, like inventory orders, technical support, phone coverage, etc.
What should be happening with these tools is a far more structured use for each (and throw in reporting as well). All too often these tools are used without discipline which leads to mulitple versions of the truth, lack of focus, red herrings, miscommunication, and ultimately a waste of time and energy.
IT and business users need to work together to better understand what each tool can provide, when that tool will be used, how it will be used, how it will NOT be used, and who should be using them.