A "kissing cousin" is any cousin that is not a first cousin. In most places in the world, first cousins may not have sex and have babies. But, in most cultures second cousins, and higher can have sex and babies. Degree of cousinship is determined by how many generations the shared ancestor is removed from the individual closest to the generation of the shared ancestor.
If we share the same grandparent we are first cousins, and therefore should avoid physical encounters with each other which might lead to sex. First cousins are NOT "kissing cousins." If we share the same great grandparent we are second cousins and are therefore able to kiss and do whatever we want, including having sex, and have babies together.