What is the exact meaning of vicinity of Black hole or a disk? the same as inside? What is the exact meaning of vicinity of Blackhole or a disk? Is this the same as inside the horizon for black holes? If so, why people don't say inside of BH, simply. What is the difference?

I use this phrase actually! and it may seem obvious but not to me, please somebody make it clear. I searched but I couldn't find an exact answer.

Edited: Until which radius from Blackhole I can use this word meaningfully? It's not clear to me its astronomical dimension. "near" is not enough to me. If it could be inside a horizon and also outside of it, it makes a huge difference from point of view of the observer at infinity, as you know, how I can call them by the same name and sometimes I mean one sometimes the other one.
From the Oxford English Dictionary:


  "vicinity" just means "the area near to or surrounding a place" 


so "in the vicinity of a black hole" just means "near to a black hole." 

Other dictionaries say "immediately next to" so in response to your comment about vagueness, treat vicinity as the immediate neighbourhood of the black hole. You will not find an exact meaning - it is used as it is in English. There is no specific distance measurement. You don't have a distance from radius which would stop being in the vicinity.