Citizenship of the United States
A person who is considered a citizen by more than one nation has "dual citizenship". It is possible for a United States citizen to have dual citizenship; this can be achieved in various ways, such as by birth in the United States to a parent who is a citizen of a foreign country (or in certain circumstances the foreign nationality may be transmitted even by a grandparent) by birth in another country to a parent(s) who is/are a United States citizen/s, or by having parents who are citizens of different countries. Anyone who becomes a naturalized U.S. citizen is required to renounce any prior "allegiance" to other countries during the naturalization ceremony; however, this renunciation of allegiance renunciation of citizenship to those countries.
Dual intent
Dual intent is a United States immigration law concept. It generally refers to the fact that certain U.S. visas allow foreigners to be temporarily present in the U.S. with lawful status and immigrant intent. This allows those visa holders, particularly H-1B professionals, to enter the U.S. while simultaneously seeking lawful permanent resident status (green card status) at a port of entry. Otherwise, visa holders may be presumed to have immigrant intent and can be kept from entry (summarily excluded) as a matter of law.