enotstrebor said:
Matter has mass (see http://en.wikipedia.org/wiki/Matter" ), but maybe it is different in your circle of friends.
However, energy and mass are not the same thing!
The photon has energy but no mass. A massed particle has energy but has massed properties which are different than photon properties. Mass can travel at any velocity less than "c" and requires energy to change its velocity, while the photon only wants to travel at "c''.
As massed energy and photon energy behave differently, energy and mass can not be the same thing.
E=mc^2 says that there is a relationship between the two not that they are the same.
There are several definitions of matter in that wiki article. Also think of this, a container with photon gas will have mass and a volume -> will one call the gas matter, and the constituients "non - matter" ? One has probably the same problem with the dark matter, we don't know what it is made up of - why do we call it matter then? Well it has mass and volume one might say, but that has the photon container also..
So, again to answer OP's question if the fundamental particles are considered as matter, it depends on what definition of matter you employ. The definition "everything that an atom is made out of" then only electrons, protons and neutrons are that for sure. But protons and neutrons are not fundamental particles, they are made up by three valence quarks each, and an "energy soup" of virtual quark- anti quark pairs and gluons (but virtual particles don't exists). Hence neutrinos, tau lepton, muon, photon etc, does not made up atoms are and are then not called 'matter' if one employs that definition.
Now energy, work in the units where c = 1, E = m .. got ya! (I work with them all the time..) What the equation tell you is the relation between mass and energy, energy can not be created nor be destroyed, it can only transfer between different KIDS of energy. Mass is one form of energy, angular frequency of electric and magnetic field waves propagating at the speed of light ([tex]E = \hbar \omega[/tex] or, working in units of [tex]\hbar = 1, E = \omega[/tex]). The c and hbar are just conversion factors in the SI system, but such constants are just a choice of gauge - physics is independent of such choices.
So what if 'massed' energy and 'photon' energy behaves differently, all forms of energy behaves differently in some way. What you have shown is just that an electron and a photon have different kinematical properties due to their rest mass. Nothing more.
I could impose that argument in a reverse order. "Now since photon energy behaves different that mass energy, photons can't be energy."
Late edit: Why u think one calls the equation E = mc^2 "mass–energy equivalence formula" ?