Energy is stored in different ways:
Kinetic — energy of moving objects
Thermal — related to temperature (internal energy of particles)
Gravitational potential — stored in raised objects
Elastic potential — stored in stretched/compressed objects
Chemical — stored in food, fuels, batteries
Nuclear — stored in atomic nuclei
Electrostatic — stored in charged objects
Magnetic — stored in magnets
Energy is transferred by: mechanical work (forces), electrical work (charges), heating (conduction, convection, radiation), and radiation (light, sound).