The U.S. Government offers protection to those fleeing political, religious, or social persecution under two basic sets of laws: refugee law and asylum law. The legal test for both groups is the same – both must prove a "well-founded fear of persecution" for their political opinion, race, religion, nationality or membership to a particular social group in their home country. Individuals who apply while they are in the United States are asylum applicants.
Be aware that though someone has suffered persecution in his/her home country and are now in the U.S., it is not a “given” – guaranteed -- that the individual will get asylum.