Self, you won't be DQ'd if you sign for higher, but the higher score will stand. Sign for a lower score and you're out. If you have your caddie keep your score, you and the caddie need to sign and you need to verify the scores.

Now that's all for stroke play. Not sure what the differences are for Match play. If I "win" a hole but record the wrong score, do I lose the hole or am I DQ'd?

The rule giving information in match play is 9-2.
A player in a match is always obliged to give correct information about the strokes, taken during the play of a hole, 9-2a.
If the player gives wrong information after the hole is completed, it depends on the result at that hole.
If the wrong information affects the opponent's understanding of the result of the hole, the player loses the hole unless he corrects the mistake before any player makes a stroke fom the next teeing ground, 9-2b (iii).

It doesn't matter if the player gives wrong information deliberately or if he just forgets to count a penalty stroke, he has taken before.

McFade