Debt is the net cumulative borrowing - debt - since some established baseline, like a government's inception. It's a running total of the difference between the amount of revenue (taxes and fees) collected and the amount of money borrowed. The current federal debt, for example, is about $12,000,000,000,000 (12 trillion dollars).
The deficit is the amount of debt incurred in a year's time. It's the difference between the amount of revenue collected and the amount of money borrowed in a year. The current federal deficit, for the year to date, is $1,400,000,000,000 (1.4 trillion dollars).
The budget deficit value is added to that running total of debt to calculate the new total of debt at a given year.
So, if you spent more money than you had in a year - let's say you made $60,000, but you spent $70,000 - your deficit would be $10,000. But, that's not necessarily your debt. If you've done the same thing for the past 5 years (inclusive), your debt would be $50,000.
The deficit can be looked at as a measure of how much money the government is currently spending. Deficit values mean the government is spending outside its means; surplus values mean the government is spending less than the amount of taxes its collecting. The rate of change of the debt can be looked at as a measure of the acceleration - or deceleration - of the year-over-year spending of the government.
A key fact to remember is that that total debt must eventually be repaid. Those loaning the money always come to collect, sooner or later. But the government doesn't have coffers of gold it can draw on to settle the bill; it must collect the funds from its constituency. That means you, and every other citizen like you, are the people really holding the bill. The debt hasn't been called in yet, which means that the bill may be passed to your children, or even their children - but make no mistake, it will eventually be repaid.
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