Hi... you sort of have a double tipped question here... so I'll try my hand at one at a time...
1.) When moving files from one directory to another, IF BOTH FOLDERS ARE ON THE SAME HARD DRIVE, it will move (not copy). But if the Host folder is on one drive and the Recipient folder is on a different drive, it will copy and leave the original in the Host folder.
What you can do is using two Finder windows drag the file(s) into the other folder and before released the mouse, hold down the Control Key as you release the mouse and they will move... not copy.
2.) The way I find all video or other "same" files is to do a search in Finder i.e.... if the videos you are looking for are .mkv files then do a search in Finder for .mkv files... I usually try to make sure I am in root of the drive I am searching just because it makes me feel like I am getting a complete search, although I don't think that matters.
There is also third party software that will do this and I have tried them but never use them.
Hope this helps!