Original sentence: However, some modern bitless designs of horse headgear lack the heavy noseband of a true hackamore and instead work off of straps that tighten around a horse's head to apply pressure in various ways.The hackamore, is headgear that controls a horse without a bit,  but to call it "bitless bridle," is incorrect other than as a descriptive simile, as the hackamore predates all other modern bitless designs by several hundred years.The term hackamore is the most historically accurate word for most common forms of bitless headgear.These are often specifically patented and marketed as "bitless bridles," usually referencing a particular type of headgear known as the cross-under, though other designs are sometimes also given similar names
Edited sentence: However, some modern bitless designs of horse headgear lack the heavy noseband of a hackamore and instead work off of straps that tighten around a horse's head to apply pressure in various ways.The hackamore, is headgear that controls a horse without a bit, and is as such under the newer design based category of Bitless bridle, even though the hackamore predates all other modern bitless designs by several hundred years.The term hackamore is a subcategory of bitless bridles and the most common form of bitless headgear.These are often patented and marketed under the category "bitless bridles," usually referencing a particular type of headgear known as the cross-under, though other designs are sometimes also given similar names