A full breed is a term used to designate a Creature breed with a new genome and new sprites, which requires a breed slot of its own. New full breeds are relatively rare by comparison with genetic breeds, which have new genomes and often new behaviors, but create their appearance from the sprites of existent full breeds. This may be due to the enormous task involved in creating the hundreds of sprites needed by a full breed.
In fact, the Creatures Wiki page for breed describes a full breed and will contain more information on them.
Also, consult the Genetic Breeds Category.