Of course, but in different states. This was one of the 5 breakthroughs Einstein made. When we figured out how to convert matter to energy through fission and subsequent chain reactions, we confirmed Einstein (again) and released the energy of matter - we created nuclear energy - used for bombs and power plants (we also figured out how fusion works - but we have yet to create a fusion reaction - this interplay between fission and fusion is how the stars function - like our sun). This is called the "mass-energy equivalence" found in Special Relativity and expressed by the famous "E = mc^2" (energy measured in mega-joules - or higher - depending on the amount of mass - in the sample - equals the mass of matter multiplied by the speed of light - squared - that's a lot of energy). The laws of conservation of matter or energy hold true for both - neither can be created or destroyed, only changed in physical systems. We have one subatomic particle of matter that is almost mass-less that passes through everything - including us - all of the time: neutrinos - but despite their mass never being measured - because it is so small - it still has mass and is matter. Classical Newtonian physics defined inertia differently than what Einstein advanced upon - by introducing reference frames - and the concept that space and time were "interwoven" as space-time, which curved under the influence of gravitation.
They are not the same thing because mass has inertia, energy does not. Mass is measured in kg whereas energy is measured in Joules. Matter and energy actually aren't in the same class and should not be paired in one's mind.