K-2 visas are for minor children of the K-1 visa-holder who are eligible as derivatives for admission.
K-3 visas are for people already married to U.S. citizens, where the U.S. citizen spouse has filed an immedaite relative immigrant petition, and the beneficiary seeks admission while awating its approval.
K-4 visas are for children of K-3 visa holders. K-3 and K-4 visa-holders are admitted for two years and they are not eligible to change to another nonimmigrant status.
V-1 visas are similar to the K-3 visas except that it is for someone who is married to a Lawful Permanent Resident (LPR), who filed a family petition on his or her behalf before December 21, 2000, and the petition has been pending for three or more years for any reason.62 This visa is also for a person who has been waiting for three or more years for approval of a family based immigrant petition due to the lack of availability of an immigrant visa because of quota restrictions. The V visa appicant is not subject to the inadmissibility grounds due to unlawful presence or illegal admission to the United States, but must seek a waiver when he or she applies for adjustment of status.
V-2 visas are for the children of the V-1 visa-holder.