It does get confusing...I know you didn't ask me the above question but come to think of it, I have no idea what brand my brackets are. I have ceramic (clear) on the top 6 and metal everywhere else.
Braces behind the teeth = lingual or ibraces
Braces that look like a clear mouthguard = invisilign
Any type of bracket worn on the front of teeth = different brand names, such as: damon, clarity...these can be metal or clear (ceramic)
You can also ask to see the brackets they use. I suggest to everyone, while you're at the office, see if you can check out what the patients have. This way you can get a better understanding of what they offer.
I still think the $700 is too high, maybe see if you can negotiate especially since he isn't a certified ortho. Or do they have certified ortho's there? Then again, maybe paying the $700 will kick your bum in gear to get the braces because we all want you too!
). 
. My mother picked up on it and took steps to put me on my orthodontic journey 
. My front teeth were crossing over each other and pushing outward and my bottom teeth were crossing over each other and pushing forward. 
