What is the difference between a budget deficit and the national debt?

The basic difference between these two things is that a
budget deficit is only about one year while the national debt is
cumulative.

The budget deficit is the difference between
the amount the government receives in revenues in a given year and the amount that it
spends in that same year.  When the government spends more than it gets, it has a budget
deficit.

When the government does this over a period of
years, the deficits build up.  When you add the deficits from each year (plus interest
and minus any payments that have been made) you get the national
debt.

So the debt is, essentially, the cumulative total of
the deficits from all the previous years.