K1 visa are temporary immigrant visa for family members that allows the fiancees of U.S. citizens to come to USA and marry the citizen. After issuing this type of visa, married spouse can apply for a green card through marriage and remain in the United States during the time until this petition is approved. K1 visa is available only for fiancees of U.S. citizens living outside the USA.
K3 visa are temporary immigrant family visa, which allows spouses living together in a waiting period for a permanent spouses visa (I-130). Spouse of the U.S. citizen for whom the immigration process begins in the US is not required to obtain K3 visa. K3 visas are available only for legitimate partners of American citizens living outside the USA.