Natural honey is a redundant description of honey since, by definition, honey is only naturally produced by bees. For honey that is produced as closely as possible to the way bees make it see raw honey. Natural may also refer to the method of farming. Some types of bee farming certification are referred to as natural, see organic honey.
Conversely, there are some ‘unnatural’ honey replacements that attempt to be similar in taste and texture to honey. These are sometimes referred to as imitation, artificial or synthetic honeys. One is Invert sugar made of table sugar and citric acid. It is similar to a very simplified form of honey which is an invert sugar formed by the enzyme invertase from nectar gathered by bees. Another cleverly uses Fireweed and Clover blossoms to create an imitation honey recipe for Alaskan Fireweed “Honey”.