In Germany and Switzerland, the acronym GmbH is used for private companies, while the letters AG are used for companies that are publicly traded. A GmbH company is a limited liability company, while an AG company is considered a joint-stock corporation.
GmbH stands for Gesellschaft mit beschränkter Haftung, which literally translates as "company with limited liability." AG is an abbreviation of Aktiengesellschaft, which is the German word for corporation. In order for a company in Germany to qualify as a GmBH, it must have a minimum of two partners and be incorporated, meaning it is a legal entity unto itself. The company can be owned by a public company, although this is not a requirement.
Each country has its own specific definitions and requirements for each of these types of companies. In many countries around the world, privately held companies are given the designation S.A. There are a number of different meanings for this abbreviation depending on the country in which the company originated, but in English it loosely translates to "anonymous society."
In addition to GmBH, another one of the more common designations for publicly traded corporations where the owners have limited liability is PLC, which stands for Public Limited Company.