The three phrases, plainly
FDA cleared: the manufacturer submitted a 510(k) showing the device is substantially equivalent to a comparable cleared device for a named indication. Most red light therapy devices that carry any regulatory status carry this one.
FDA approved: reserved for higher-risk classes and requires clinical evidence of safety and effectiveness. Consumer red light devices essentially never have this, so a product claiming it is misrepresenting itself.
FDA registered or FDA listed: administrative only. Any facility making devices registers with the FDA; it says nothing about the product's safety or performance. This is the phrase most often used to imply more than it means.