A process server is someone who takes the legal documents for a court case and delivers them to the person who is being sued, as noted by the Judicial Branch of California. This process is referred to as being "served" and it is considered proper legal etiquette to have a process server deliver the documents rather than delivery from the person who is suing.
It does not matter if the entity is an individual, a partnership, a government, a business or a corporation. Another name for a process server is simply a "server." Without "serving" the person or organization who is being sued, the judge will be unable to make any judgments, orders or decisions regarding the case.