You're a bit mixed up, but that's okay. Just forget the word 'dragon' and go with this.
The Shinzoku are the opposite of Mazoku. They're good astral beings, spirits of light. Ceiphied was one, and the 4 Dragon (forget that word) Lords he created, his alter egoes, are Shinzoku too.
The Ryuzoku are physical beings. They are what you would understand as literal dragons. They worship the Shinzoku and work as their underlings, in the same way that lesser demons are the underlings of Mazoku, in a way.
Shinzoku and Ryuzoku aren't directly related, although Shinzoku do seem to come in the shape of dragons. Then again, so did Gaav, so the shape must have some significance.
Hope that clears it up for you.