The most accurate statement regarding the energies in the system when the magnets move to attach to each other is:
The energy stored in the system is converted to kinetic and thermal energy.
When the magnets are in close proximity, they have potential energy due to their magnetic fields. As they move towards each other, that potential energy is converted into kinetic energy as they gain speed. Additionally, some of the energy may also be converted to thermal energy due to friction and other forces at play during the motion.