Most professions come with a written code of ethics. A professional code of ethics governs individuals' conduct within their profession so that their behavior is ethical, honest, and above reproach. A professional code of ethics also focuses on social issues and outlines the general principles which guide a company or an organization's beliefs. This code may be further broken into subcategories such as "code of conduct" and "code of practice." These are more specific "rules" delineating to what standards employees or organization members will be held when it comes to carrying out professional responsibilities.
On the other hand, "personal ethics" or the public's ethics could more simply be defined as a general standard of acceptable conduct within a society. While there exist specific written laws that individuals within a society will be held responsible for following, laws do not necessarily determine the ethics of the public. More often, public ethics could be considered the general and mutual consideration for what is acceptable behavior within a society. In this way, public ethics vary greatly between nations, states, cities, and even individuals.
To paint a hypothetical picture that directly contrasts where professional ethics and personal ethics could come into conflict, I think of the legal profession. Lawyers (who are governed by the bar) are bound by a professional code of ethics dictating specific rules for how they must serve their clients. Additionally, all alleged criminals are given the "right to a lawyer." A lawyer who, for example, is appointed to defend a certainly guilty offender in a court of law, may face a conflict between his professional code of ethics (which says that he must provide adequate defense) and his personal ethics, which typically condemn such members of society.