#E=mc^2# is known as the energy of being. If the entire mass was to disintegrate into pure energy (e.g. in a collision between an anti-matter and a matter particle), this is the energy which will be released into the surrounding.
#E=E_"pe" + E_"ke"# is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position). Objects have mechanical energy if they are in motion and/or if they are at some position relative to a zero potential energy position (for example, a brick held at a vertical position above the ground or zero height position).
The total energy of a system is always # E=mc^2# , but we cannot use it to solve daily life problems (like the energy of a stone held at a height) so we use #E=E_"pe" + E_"ke"# for simplicity and distingushing between # E_"pe"# and #E_"ke"#.
Also, #E=mc^2# also doesn't take into account gravity for #E_"gpe"#
