Game Capture is a capture mode/source in OBS. It hooks the game directly in video memory, resulting in VERY fast capture, especially as compared to Monitor Capture (which is slow as frozen dog**** under Win7 at least).
DXtory is an alternate for-pay capture program that essentially does a monitor capture, and pretends to be a webcam source so it can be added to casting software. As XSplit is tremendously bad at this kind of capture, many use DXtory under it to overcome XSplit's major, glaring failings. Something that isn't generally required under OBS, as Game Capture is actually faster than DXtory to begin with.
Digging up a thread from months ago generally isn't the best method to ask this kind of thing, either. :) Just saying.