Puzzle Mode and Puzzle Mode Light both remove the element of random chance from the game, focusing instead on the puzzles our hero, Burden, is faced with. Puzzle Mode retains the original difficulty of said puzzles, while Puzzle Mode Light makes them a bit easier. Narrative Mode is the easiest of the bunch, as it turns the game into a narrative experience, "without a heavy challenge," according to the game's Steam page.
Apart from introducing new difficulty levels, The Mercy Update includes a number of bug fixes, including one where a woman would come back to life if her child was threatened. The mercy bestowed by this update, in other words, is not for all. Sorry, immortal mama.