There is a difference. The media often mixes up the two. It is important to understand the difference.
Federal Budget Deficit/Surplus is the difference between tax receipts and expenditures for a fiscal year. When tax receipts are more than expenditures there is a surplus and when tax receipts are less than expenditures there is a deficit. The fiscal year for Federal Government is October 1 to September 30. For instance, right now - January 27, 2010, Federal Government is in Fiscal Year 2010.
The President submits the budget request to Congress for approval by the first Monday in February before the new fiscal year starts in October. Congress receives it and has hearings to question administration officials about it. Then House and Senate develop budget resolutions to pass by each body separately. After passages, both chambers of Congress meet to reconcile the differences and arrive at one budget resolution. Congress can enforce the adopted budget resolution through the ability of a single member of the House or the Senate to raise a budget “point of order” on the floor to block any piece of legislation that violates (or exceeds) the budget resolution. There are serious questions to the effectiveness of this enforcement mechanism.
Our current budget deficit for Fiscal Year 2010 (projected) is $1.3 Trillion. The last time we had a Budget Surplus was Fiscal Year 2000: $86.4 Billion. What happened: 1) Bush’s tax cuts; 2) Iraq and Afghanistan Wars; 3) Wall Street Bailouts and 4) the effects of the Great Recession - in the form of much lower tax receipts:

Source: Center on Budget and Policy Priorities
Federal/National debt is the amount debt issued by the federal government. Some people define it in terms of funding of federal deficits. The problem with that definition is that federal debt is issued regardless of whether there is a budget surplus or budget deficit. Currently, the outstanding amount of federal debt is $12.3 Trillion. A good way to put this amount in perspective is to compare it to the Gross Domestic Product(GDP) or make it a percentage of GDP:

Source: ZFacts.com
Notice the red lines! So much for Republicans being fiscally responsible.
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