Trading goods and services without the use of money is called bartering. Early civilizations relied on this kind of exchange. Even cultures in modern society rely on it. Think of people in prison who commonly trade cigarettes for protection or extra food. For the most part, they don't have cash. So, like people in pre-currency economies, they work with what they have.
On paper, this sounds a bit like delayed barter, but it bears some significant differences. For one thing, it’s much more efficient than Smith’s idea of a barter system, since it doesn’t depend on each person simultaneously having what the other wants. It’s also not tit for tat: No one ever assigns a specific value to the meat or cake or house-building labor, meaning debts can’t be transferred.