A deficit is usually considered to be the difference between the revenue generated by a business (the money you take in) and the expenses of that business (the money you spend). A deficit can be real (e.g., spending decisions have been made, and now you need to find the funds to cover the deficit), or the deficit can be projected (e.g., your cash flow projection tells you that you will have a cash shortage next March), in which case you can plan a strategy to address that issue before it becomes a cash emergency. If you fall into a cycle of deficit spending (not having enough cash to pay the bills), you could find yourself "in debt."
Debt refers to money that you have borrowed or owe and have promised to repay (for loans, that includes interest). Debt management refers to the strategies you put into place to manage your debt and ensure that you can meet the required repayment schedule.
Another way to think of these terms is that deficit is a condition―more money is going out than coming in. Debt is a tool―a method of leveraging someone else's capital to meet your cash needs.
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