Trade refers to the buying and selling of goods and services, facilitated by a medium of exchange, such as money. When goods and services are exchanged for other goods and services, without the use of money, then we have a barter form of trade.

Business, on the other hand, refers to all those activities that are done with the aim of making a profit. As such, it includes business operations such as producing and selling goods or provision of services, investing activities such as the buying or selling of long-term assets, and financing activities such as the issuance of shares or bonds, repurchase of company stock and payment of dividends. Therefore, trade is a component of the business activity.

A business can also be defined as an organization where goods and services are exchanged for one another or for money.

Business refers to the process of being involved in both commerce and trade to earn a profit. It involves the selling of goods, services, or information by one person to other people and is usually found in capitalist countries. Trade is a subset of business that involves buying and selling and in which one purchases goods or services from another person and pays for them. Business includes not only trade but also commerce, which refers to other activities involved in business, including advertising, purchasing, operations, finance, and so on. In other words, business is the entire enterprise of making, selling, and controlling the production of goods, while trade, a narrower activity, involves only the buying and selling of goods. Trade is a part of business, but business is not the same as trade.

At least as used in the United States, these two words are used in so many different ways that it is impossible to really tell the difference between them.  At times, they can mean the same thing, at times not.

• Business can refer to an actual firm, trade cannot.  You can say "the business that he runs" but not "the trade that he runs."
• Trade usually refers to imports and exports.  If you use the word in the US, that is what is people will assume you mean.
• For commerce in general, Americans usually use the word "business."  We say "business is picking up in the service sector."

But some of these things, at least, are used differently in England, at least, so depending on where you are, this answer may not be accurate.