Here are the vocabulary terms related to trade and payment methods you've described:
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Barter: Paying for a good for another good (exchanging one good or service directly for another without using money).
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Check: Paying for a good with a signed paper that a bank exchanges for money (a written order directing a bank to pay a specific amount from one account to another).
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Credit: Paying for a good after receiving it; a promise to pay (involving borrowing funds from a lender with the agreement to repay it later).
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Cash: Paying for a good with physical money (coins and banknotes; tangible currency used for transactions).
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Currency Exchange: The process of converting one form of currency into another, often for the purpose of trade or travel.
If you need further clarification or additional terms, feel free to ask!