Conventional handicap uses the rank difference (and the board size) to set the handicap. Komi is 0.5 for uneven games and 6.5 for even games. The board size is independent on this. So the komi would be the same 6.5 on a 9x9, 13x13 or 19x19 goban.
 
Proper handicap uses finer komi intervals (..., 1.5, 2.0, 2.5, ...) to balance minor rating differences to a 50:50 chance for both players.