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.