The term kissing cousins has many definitions. Its meaning is conveyed by connotation according to the setting in which it is used. Depending on cultural environment and mood of conversation, its connotation can be humorous and good natured, pejorative and nasty, or simply informative. The meaning is left to the discretion of the one hearing the term. It can also be used to indicate a relationship or similarity between things rather than human beings.In the first sense, it could either mean people who are closely enough related so that a kiss is an acceptable form of greeting or, in some states, that they are not so closely related that kissing might lead to an incestous outcome and could therefore be cousins but not a first cousins. These would be people who are allowed by law to get married and have children.
In the second sense, when used pejoratively to denote something base, immoral, and incestuous, it implies that close relatives are sexually active and will produce or have already produced a crop of imbeciles or physically altered mutants. About half of the states in the U.S. ban marriage between first cousins for that reason, but modern science has shown that there is only a very little increased risk of inherited disease or abnormalities when first cousins have children.
That's not to say that there is no risk in groups that are known to have high incidence rates of genetically transmitted conditions like Negroes with sickle cell anemia, Jews with Tay-Sachs disease, or Northern Europeans with hemochromatosis. First cousins in groups where any hereditary condition is prevalent and who intend to marry should get genetic counseling beforehand. The state of Maine, in fact, requires first cousins to do so before they can be legally wed. Still, the risk is only slightly higher than it would be if the couple were not cousins.
There is the rare case of double cousins which are are first cousins who share two sets of grandpaents. That occurs when siblings of one family marry siblings of another family. As far as marriage laws go, North Carolina is apparently the only state than allows first cousin marriages but bans double cousins from marrying. Other states that allow first cousin marriages do not make a distinction for double cousins.