Peace All
The green turban people are called Dawat-e-Islami, they are barelvi by fiqh and I believe they are Qadri by tariqah. Not all qadri barelvis belong to this group, their identification of the green turban is due to their specific sheikh - who represents Dawat-e-Islami.
Likewise not all Deobandis are from tablighi jamaat. In fact, a local imam (to where I work) is a Deobandi by fiqh and Naqshbandi by tariqah. Tablighi jamaat are not an official tariqah, but their activities do include some tassuwwuf.
I have a beautiful friend who is Barelvi by fiqh, Shadhili by tariqah, but he attends Tabligh on occasions. When we see people who search for wherever they can get goodness from these are the people who we need to appoint as our leaders.
Incidentally Maulana IsHaq - an Ahl-e-hadith (wahabi-hanbali) pakistani Imam calls both Deobandis and Barelvis brothers in Islam.