Answer:
A budget deficit is one element of some budgets but is not a "type" of budget. You may be thinking of a "deficit budget" (see below). To start: a budget is simply a spending plan - how much the government is going to spend over the next budget period (often a year), and on what. This includes interest the government has to spend on money it has previously borrowed (usually through bonds).
If the total to be spent is expected to exceed what the government expects to take in (usually through taxes), the difference is the deficit, often called the "budget deficit". On the other hand, if the government expects to take in more money than it spends, the difference is a surplus, called the budget surplus. A budget that has a deficit is a "deficit budget"; one that has a surplus is called a "surplus budget"; and one that has neither (that is, spending and income are equal) is called a "balanced budget".
It's worth noting that "deficit" and "debt" are not the same. The deficit is the amount by which the government overspends its income in a single budgetary period, typically a year. The debt is the total amount of money the government owes, and can be calculated by adding up all the budget deficits and surpluses the government has ever run.