TimeShift is easier to understand, because pretty much every FPS dealing with time mechanics has been doing it that way: you have a suit that "controls time" in a general-except-for-you manner. You can slow time, à lá F.E.A.R., and also freeze and rewind time (apparently you can actually use what version of the power you want, I was under the impression it was preset according to the situation). And that's it. It's basically a F.E.A.R. clone with worse gameplay and, oddly enough, looking way worse, despite having been released two whole years after F.E.A.R.

Singularity has a "focused" time mechanic system, instead of a "global" one. Instead of moving time all around you, while you are unaffected, you use time "powers", that you aim and focus one item (or two) at a time. You can age items and enemies forwards or backwards (repair or collapse stairs and machinery, destroy enemy cover, open safes by aging the door to a point that the hinges just fall off, aging an enemy until it's nothing more than a pile of ashes -- or, if it also has some sort of time control power, slow it down --, etc); you also have a stasis field "orb" that you can throw or drop and use as a shield or to solve puzzles, since everything it touches stops (good for those annoying spinning fans you can't turn off :P ); there's a "time pulse" that replaces your melee attack early on, which you can use to "shift" some enemies into the time you're in, break some objects, knock back, stun and -- with enough upgrading -- downright slaughter enemies; an ability to pick up, carry, drop and throw items, kind of like Half-Life 2's Gravity Gun; two sniper weapons have time-related mechanics, too, the first one is a basic sniper rifle that lets you slow down time and the second one severely slows it down while you take control of a bullet in flight.

I know most people don't find any of this impressive or cool, but I actually prefer it to the stale system TimeShift uses. From comments I've been reading in here, it's not that impressive because it's just "winding time back to fix stairs and machinery". And, yeah, that's not wrong, a big part of the game is spent doing just that. But the time mechanics allow for a lot more than just fixing stairs and machinery (or aging them so that they get destroyed, by the way; some puzzles actually require you to wind time back and forth). Sometimes you'll also need to stop time. Other times you'll need to use pulse. Or use the special sniper rifle in which you control each bullet as you fire them. I guess fr33kSh0w didn't play much Singularity, and thinks a 46 minute gameplay video on Youtube "shows all the gameplay there is to show" (spoiler: it doesn't).