Thermal energy is defined as a molecular motion. It is measured by the metric we call temperature.

Obviously energy is involved -- but there is a difference between energy in wave forms and energy manifesting in molecular motion which may be in any pattern or no apparent pattern. Just because energy is involved does not mean that "heat is an energy wave". That concept went out when we outgrew phlogiston theory.

When you play energy over molecules they get excited, and move around, so obviously energy in wave form can induce heat--anyone who uses a microwave knows that. But to say they are the same thing is sloppy. Words fall short to the degree they are used sloppily. They can be quite good at paralleling experience, although no-one would ever claim they WERE experience.

A