A K-1 fiancée visa allows a U.S. citizen’s fiancé to enter the United States for the purpose of getting married. A K-2 visa is for the children of the K-1 fiancée so that her children can accompanying her to the United States.
The US citizen and the fiancé must be free to marry each other. The couple must have met in person within the past 2 years prior to the filing of the petition. There are exceptions if meeting was impossible due to religious or extreme circumstances. The U.S. citizen must meet the financial requirements to support the fiancé.
After the K-1 visa has been approved, your fiancé will be provided a six month single entry visa for the United States. Upon entry, the fiancé and the U.S. citizen has to marry within 90 days.
See the K-1 Visa Requirements from Siam Legal website.
A K3 visa is under a non-immigrant visa issued to a spouse permitting her to enter the United States. There must be a pending immigrant petition filed by the U.S. citizen for the Thai spouse.
The K3 visa is multiple entry two year visa. K3 visa holders can enter and exit the United States as many times as they wish as long as their visa remains valid. The K3 visa is valid for 2 years, and can be renewed in two-year increments while your spouse applies for permanent residency. The benefit of a K3 visa is that it is the fast way for the spouse to enter the United States.
See what is a K-3 Visa from Siam Legal website.
Upon entry into the United States, the K3 status holder has to apply for adjustment of status to obtain permanent residency status. If the pending immigrant petition at the USCIS is approved prior to the fiancé petition, the fiancé petition will be closed in favor of the immigrant petition.