Most small businesses choose the legal business entity of a "sole proprietorship", where one person is the only "owner" of the business. Legally, there is no difference between you and your business, and while this business entity type is preferred by some because of the ease in setting it up and registering it, there is a greater legal risk assumed by the owner of a sole proprietorship. For example, if someone sues your business for infringement or fraud, they will be suing you, and your personal assets will be on the line if the case is taken to court - a disadvantage to this kind of legal business entity. This type of situation is rare to be sure, but from a business standpoint, it has the potential to be a risky move.
Limited Liability Company (LLC)
Finally, a Limited Liability Company (LLC) is a sort of combination of all of the above business structures. Like the "corporation" business entity type, an LLC offers a legal distinction between a person and their company, but like a sole proprietorship or partnership, it offers the owner or member (we're back to being called members now) control over business decisions, tax breaks, and offers no stock option. There is no limit to how many members an LLC may have, and it is also possible to just have one member. The obvious upside to this type of legal business entity is that it provides the best parts of both worlds, corporation and non-corporation, but the downside is that it is more difficult to file than a partnership (but is still less difficult than forming a corporation). To date, the federal government does not recognize an LLC as a classification when you file your federal taxes, so you must file either as a sole proprietorship, partnership, or corporation.