This is a separate class of honey called Honeydew which is relatively uncommon in North America as far as availability goes, and is often referred to as "Forest Honey" in Europe.
The origin of this unique honey and its name does not relate to the Honeydew plant but rather to the ancient beliefs regarding a "honey dew" falling from Heaven, or "Manna." Aphids and other scale insect feed upon the sap of trees and plants. They exude most of this, and sometimes when the exuded sap would collect on leaves and then fall with a rustling breeze, people in ancient times thought honey was falling from heaven, thus, a "honey dew." In times of drought when floral nectar sources are scarce, bees will forage upon these exudations and make a beautiful honey from it.
Honeydew Honey is darker in color and has more mineral content. It has a smooth, semi-sweet flavor with woodsy, malt notes.