Certified GKH Gardening Expert
The "Honeysuckle" Azalea is, simply, another cultivar of Azalea. It is not a Honeysuckle. The same goes for "Mollis" Azalea. These are just two different types of Azaleas.
The Honeysuckle is a different plant altogether. Honeysuckle is part of the Genus, Lonicera. Azaleas are of the Genus, Rhododendron.
This article will give you more information on growing Azaleas: