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No PaulB - totally different.
The deficit is the amount spent day in day out in excess of income.
This is like having an income of £2,000 a month and spending £2,800 a month with the difference being added to the credit card and paying off only the minimum as part of the £2,800 you are spending. In doing so you are building up debt that has to be serviced and that adds more and more interest increasing the deficit even further.
Debt is the amount of capital you owe - different.
The problem is this...
According to Keyseyan economic theory (much applauded by Labour) you can increase the deficit in the bad times to cover the fall in tax revenue and pay for increased out of works benefits and possibly some infrastructure projects to help 'stimulate' the economy. So far so good.
The problem was that Keynes also says that the deficit should be reduced/balanced and debt repaid in the growth part of the economic cycle.
It is the latter part Labour ignored and did the opposite.
Look at what happened in the 1990 recession, a deficit was allowed to grow in the Keynseyan style and was starting to be reduced during the recovery, by 1997 when Blair/Brown were elected, Ken Clarke was making inroads into the deficit. Indeed that deficit reduction, fuelled by economic growth was subject to an election pledge by Brown to carry on limiting spend plans to those planned by Ken Clarke. Spending through to 2001 by Labour, at least what was 'on balance sheet', did indeed meet that pledge and the deficit carried on reducing and was on course to be eliminated by the next cyclical downturn. (I will not get into Brown's off balance sheet fiddling here). Once the period of the spending pledge was over Brown reversed policy and started increasing spending and reversed the deficit reduction. By 2007 when the downturn started the economy was already struggling under the weight of a massive deficit so that the economic damage (acknowledged by Darling) of not addressing it was worse than that of reducing the deficit during the downturn.
Ideally you would not reduce spending in a downturn but when you have the starting point of a massive deficit already then you have no sensible alternative but to cut it.
I have said it before... Brown boasted he had 'banned boom and bust' and ran the economy as if he really had, to all our cost.
Remember - the economy always works in cycles of growth and contraction, it is like a law of nature. In the growth phase and when things are all going well it is the time to prepare for when things get worse, build up reserves and get rid of debt. That is what Brown failed to do, he did the opposite.