No doubt it has origins in deoband school (in reality from the sunnah:)).. but when I say “not all tablighis are deobandis and not all deobandis are tablighis” I mean, not all those who go in tabligh associate themselves with Deoband and not all those who associate themselves with Deoband go on tabligh.
Example, tablighis are all over the world, you get Arabs, English, Africans…etc not all are deobandis 
Example, some deobandis go on tabligh, some focus on tasawwuf, some on fiqh..etc not all are tablighis.
*tablighis in the Tablighi Jamaat sense.