The DEFICIT is the difference between what the government takes in and what it spends, period. Historically, the US spends more than it takes in. For a while in the late 1990's, we had a surplus, not a deficit which meant the government receipts (taxes, fees, etc) were actually more than what we spent.
DEBT is a financial term. Companies, municipalities, cities and countries issue debt. When a bank issues debt, its usually a CD. The USA sells debt in the form of treasury bills and treasury notes and anyone can buy them, you, me, China, etc. Remember those old posters from WWII era to buy war bonds, that was debt. Parents used to buy savings bonds for their kids, that was debt. When an entity issues debt, they are obligated to pay back the principal and interest.
Currently the USA enjoys a very high credit rating for its debt which means the government can issue debt at a very low interest rate and this is a sign of strength. The deficit is a political football with both sides offering up solutions from cutting spending and increasing revenue (taxes).