The word hackamore came from the spanish word "jaquima". The hackamore is the whole setup, mecate, headstall/hanger, bosal and fiador if you choose to use one. Same as you call a bridle including bit, reins and headstall.(see first illustration below)
A hackamore does NOT include (and I don't give a sh*t what the tack store on the internet calls it) A mechanical hackamore, that crazy bear trap device that is a basically an oversized mouth shutter,(second pic below) all those barrel racer bits with a rope nose band on it(third pic below), a bitless bridle(I just recently seen these) or even a rope halter.
If it does not have a rawhide braided bosal with a rawhide core, mecate reins(even if they are the synthetic ones that are not horse hair)a headstall/hanger and like I said above a fiador(optional) it is not a hackamore.
I realize there is a huge trend to go "au naturale".... but nothing is truely natural. If your horse doesn't ride well in the bit it doesn't mean that riding without one is going to always going to be the fix. There are horses that are naturals at riding in a hackamore or a halter and those that are not. Riding in this type of setup is actually harder than riding in a bit. You have to have the respect to keep him from running through it. It takes a light hand and clear mind to keep a horse good in one. They were not made to be rode in for the entirety of a horses life, merely to get him through the tough years when his mouth is changing, to preserve his soft mouth and progress him into the bridle. You can make a horse hard in the face faster in a hackamore than in a bit. The soft tissue that the hackamore rests on is just as soft as the tissue in his mouth, but toughens faster. Once he learns that he can run through it...your done. Riding a horse in a hackamore is kinda like playing Poker...it's about bluff.
If you would like a basic understanding of the hackamore, I would love to recommend "Hackamore Reinsman" by Ed Connell. It has been the bible for hackamores since the fifties and still is. This book needs to be read several times and carefully and even at that it doesn't explain it all. A basic guide, as nothing beats riding with a true horseman.