The ASTM equestrian standard is the toughest riding helmet standard in the world. An ASTM equestrian helmet is specifically designed for horseback riding and all ASTM equestrian helmets sold in the U.S. are certified by SEI to meet that standard. Horses, and the ASTM equestrian standard, are higher . Height means increased g's, or risk of severe injury, if you fall.
Some bike helmets are self-certified.
This means you take the manufacturer's word that the helmet meets the standard. For SEI certification, SEI inspects production lines and spontaneously rechecks them. To receive certification, each helmet model and size is tested by an independent lab- one with nothing to gain from passing or failing the helmet. Later, helmets are randomly checked again. I have met some of those involved in this testing and watched them at work.