This is incredible. You are thinking mass=matter. ...
If we consider the mass to include the energy, the energy adds to the mass of ...
'Mass' is not a thing in itself. It is a property of matter and do not confuse mass with matter. ...
Mivey knows he and I disagree enough
But since the typical accepted definition of Matter is "Anything that has mass" I'm not sure where making a distinction helps the subject under discussion.
Further most discussions of bosuns et al conclude that photons are energy with no mass; but general theory says without mass light can't fall into a black hole - yet it does.
Hence the whole particle/wave/energy/mass theoretical debate where:
Light is both particle and wave; And energy does and does not have mass.
In Mivey's quote above where Mass < Mass + Energy most equations presume that if energy has mass it's insignificant to their equation therefore the mass due to energy approaches zero and can be ignored.
So I have to agree with Mivey, if you want to debate whether Mass==Matter is correct then I think you have to define which system of mass equations you want to use.
Otherwise I think we need to agree that Matter is a term to express Mass without using units.