What are waves?

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My ignorance prevents me from understanding what electromagnetic waves really are. What is the difference between the color red at 670 nm and X-rays? Is it only the frequency that makes a wave more energetic (and dangerous) or also its amplitude? Why are infrared rays dangerous for the eyes, but not the colors of the visible spectrum being more energetic? What really differentiates one wave from another and why is this the case? I can't understand it.