This is why IAU's definition of planets is trash...
I worked out a system of nomenclature some years ago now...
AO 0 = possibly Black holes and other such crazy things we might find
AO I = Stellar Objects
AO II = Non-Stellar Spheroidal Objects (Shortened to Spheroidals)
AO II.a = Cryospheres
AO II.b = Terraspheres or Aquaspheres
AO II.c = Aerospheres
AO II.d = Brown dwarves (maybe)
AO III = Debris, Comets, Asteroids
AO IV = Maybe ships if ever needed ^.^
An AO II that orbits a AO I = Planet
An AO II that orbits another AO II = Moon
AOIs are objects that are Luminous and all the normal stuff that defines stars which I can't remember off the top of my head.
AOIIs are defined basically as any object that has a large enough mass to shape it into a sphere. The different sub-groups are have relationships to masses, but just looking at them you can tell what they refer. Small Frozen bodies, Medium Earthlike worlds, Large Gas Giants.
Defining like this removes the idiocy that is tha IAU standard where bodies can be Planets for a time, but then get ejected from a Sytem to become not planets and then be caught in another star system to become a planet again... but only if its orbit has already been cleared out... v.v This definition makes it clear what you're talking about and places Planet and Moon as more layman labels than real categorization as they should be regarded.
Of course the problem with referring to things like this is that it's not the standard nomenclature so noone will ever know that this is how you refer to them.