In the Press Release for the DA 645 25mm, Aero Bright is described thus:
Quote: 3. Aero Bright Coating to dramatically improve transmittance
This lens is treated with PENTAX-original Aero Bright Coating, which assures an outstanding anti-reflection performance over a broader wavelength range to deliver images that are more brilliant and in higher quality than those produced by previous models. Born as the fruit of PENTAX’s advanced nanotechnology, this exclusive coating reduces lens reflectance and greatly improves light transmittance by forming a silica aerogel layer with uniform pores on the surface of optical elements.
The key to this possibly lies in the reference to nanotechnology. Nano coatings are referred to in this article:
What does a 'nano crystal coat' do on this lens? - Photography, which details the difference between multi-coating and nanocoating, even though the specific lens referred to was a Nikon one.
Don't know about ghostless coating, although from the name that could apply to either multi or nano-coating. On the surface of it (no pun intended) the acronym "HD" is, I agree, an undistinguished term to apply to a lens coating, unless it stands for something that none of us has seriously worked out, yet.