Usually I do flat skull crushers for Triceps but I have seen some guys doing it in incline and decline way.
What is the difference between incline, decline and flat modes?
Is it same as we do incline/decline (dumbbell/barbell) press for chest?
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The main difference in the various forms of the 'Skull Crusher' or Triceps Extension (or indeed the Bench Press) is the involvement different muscles. As you change your position relative to the direction of gravity, some muscles will have to work more, while others have to work less.
Those are notably the chest muscles:
Notice how the neutral position works all the muscles already. So if you don't feel like either your lower or upper chest needs some extra work to get rid of disbalances, there's no need to do all of these exercises, as some bodybuilders might suggest.
Note that you could also use different grip width, or an inverted grip to achieve similar effects without a variable bench.