Mass
The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
Mass in special relativity
It is often convenient in calculation that the invariant mass of a system is the total energy of the system (divided by "c") in the COM frame (where, by definition, the momentum of the system is zero). However, since the invariant mass of any system is also the same quantity in all inertial frames, it is a quantity often calculated from the total energy in the COM frame, then used to calculate system energies and momenta in other frames where the momenta are not zero, and the system total energy will necessarily be a different quantity than in the COM frame. As with energy and momentum, the invariant mass of a system cannot be destroyed or changed, and it is thus conserved, so long as the system is closed to all influences. (The technical term is isolated system meaning that an idealized boundary is drawn around the system, and no mass/energy is allowed across it.)