Energy can be described in many contexts, such as the energy required to move something - be it translational or rotational - being kinetic energy, temperature/heat, electricity, light, etc. However, many energies learned of at a young age are simply multiple forms of a single energy. That is, heat and movement are the same thing, the former being movement on a micro scale, the latter being on a macro scale. Similarly, electricity is, to my understanding, due to the movement of electrons, and light is the movement of photons.
As an aside, primarily to add details I've yet to properly organize, there are a number of thoughts I've considered. For one, we consider energy as measured in Joules. The formula for kinetic energy ($K = 1/2mv^2$) is mathematically the integral of momentum with respect to velocity ($p = mv$). This implies to me that energy is directly related to momentum, which relates mass to motion. However, light is considered to be massless, yet has energy. Specifically, I read somewhere in my searches on the topic that light, though massless, will add to the effective mass of a container. But my considerations would be that either 1) light does have mass, but simply the smallest possible mass, or 2) light is not adding to effective mass, but rather "applying force". My searches have indicated that light does transfer momentum, but to my basic knowledge momentum measures mass and speed, which would imply that the former (light having mass) would need to be true. Perhaps the energy of light is proportional to its frequency, given gamma rays are, to my knowledge, more energetic than radio waves, and the electrons of a chemical give off different colored photons based on the degree of energy state changed. On a separate note, I've found mention that the curvature of spacetime due to matter will cause objects to accrue motion, as even if the object technically isn't moving, the spacetime is.
All this to say, it would seem reasonable to me to say that all energy is simply some form of motion, be it the motion of an elementary particle, or motion of atoms on a micro scale, or motion of objects on a macro scale. However, it seems possible that there are nuances I'm not considering or otherwise am unaware of that would indicate that energy is its own factor separate from mass and spacetime rather than a combination of the two.
Simply, is energy equivalent to the motion of matter and subsequent transference of that motion, or is that not the case, and if so why?
