What two forms of energy are you talking about? Electromagnetic (EM) waves carry energy. I suppose this could be called "light energy." But an EM wave has energy. It doesn't have different types of energy. Energy is energy. Energy manifests itself in different ways, but energy is just energy. An EM wave just has energy, light energy if you like. Heat is something else. To be specific, heat means energy transfer. Heat is a process, its the transit of energy. Heat (and I'm going to be redundant now) can be transferred (that was the redundancy since heat already means energy transfer, so saying heat transfer or heat exchange is redundant but that's what people say) either through conduction, convection, or radiation. The internal energy of an object depends on how much energy is transferred (heat transfer) through conduction, convection, or radiation and how much work is being done on the object. So if you like, when people be redundant and say "heat transfer" they are talking about how much energy out of the internal energy content of the body went into "energy in transit" via conduction, convection, or radiation.
So electromagnetic waves from the sun carries energy. It's radiation that we feel on a hot summer day. My skin heats up. Again, "light energy" or "radiation energy" is just energy. The atoms in my skin start gaining energy from the suns rays. My skin gains energy, and the energy in the suns rays provided that energy. If you like, light energy went into the internal energy of the skin (kinetic energy of my skin atoms).
Think of energy in an EM wave as water in a bucket. Water in the bucket is just water, there aren't different types of water, just water. Energy in the wave is just energy. Energy can be transferred (water poured from one bucket to another). Energy can manifest itself. If an object has 10 joules of energy, maybe 8 joules manifest itself as the motion of the object and 2 joules represent the gravitational potential energy of the object. However, it's all just energy in the end: an invisible "fluid" that things can possess and can be transferred. To pound the point further, "light" energy, "heat" energy or more specifically "internal" energy, "potential" energy, are all "the same thing." They are all just energy. After all, light energy and kinetic energy don't use different units. Both are measured in Joules or whatever energy unit you want. The adjectives that we tack on are just descriptives to highlight the situation. So saying "light" energy we mean ok, an EM wave. Saying "gravitational potential" energy we mean ok, there is a gravitational field. "kinetic" energy, ok there is some type of motion.
Side note not meant to confuse you:
Heat is a confusing word because one, colloquially, it's tied to temperature and how hot things feel. There's also the more scientific definition, which is that heat is "energy in transit." And even among scientists, we still use phrases that mix up heat and internal energy.