Budget Deficits are quoted as a specific reported figure. That number reflects the amount a government's spending exceeds its income over a particular period of time. Budget Deficits are financed by securities - debt owed to investors and owned interest payments.
Budget deficits are generally unfavorable for an economy, growth in Net Borrowing is considered bearish for a country, although the correlation is not perfect.
Deficits of course can refer to a company or individual, but references in the Forex market it will almost always refer to a country's, deficit.