I am NOT a business librarian, but I would think the difference between a business / corporate / trade name is the name by which you engage in commerce, while a trademark can be more, including a logo or design (or even soundmark or color) that is used to distinguish goods and services from those of others.
See the Trademark Searching tab on this research guide for help.
Sometimes a business name (corporate / trade name) and a trademark are one in the same, somethimes they are different.
A trademark is any word, name, symbol or device, or combination of these, used by a person (individual, partnership, corporation or association) to identify his goods and to distinguish them from the goods manufactured or sold by others. Trademarks indicate the source of goods, even if that source is unknown. Some examples of well-known trademarks are: Kodak, Coca-Cola, GE, Life-Savers and McDonalds (with golden arches).
A service mark identifies and distinguishes a person’s services and is given the same protection as a trademark. “Citibank” (Service mark for Citibank), “Greyhound” (service mark Greyhound Bus Lines), and “Hilltop” (service mark for the Hilltop Restaurant) are a few better-known examples of service marks.
A trade name is a name used by a person to identify a business or vocation of that person. A trade name may be registered as a trademark or service mark only if it also functions as a trademark or service mark.
A person may register a trademark or service with the Division if the mark is used in the Commonwealth. The use must be bona fide and not merely to reserve a right in the mark. A trademark is considered in use when it is placed on the goods or containers and tags, labels, displays or documents associated with the goods and sold or transported in the Commonwealth. A service mark is used in the Commonwealth when it is used or displayed in the sale or advertising of services rendered in the Commonwealth.