A trunnion-style ball valve has a bearing both at the top and at the bottom of the ball, so the ball rotates on a rigid axle with no deflection. Trunnion ball valve use floating seat rings to seal.
I am completely mystified as to what a pad-support is.
I think the pad support can be both floting or trunnion. At first the ball valve should be big size. And we have produced a 16" 300# ball valve for Cryognic service. At first our design is trunnion but we found is very hard to seal after tested once. Then we changed to floating but the trunnion support still here. Just done some work on ball. Hoping this can help you.
I think you must mean Floating Ball valve. A Floating ball valve has no support under the middle of the ball. The bottom of the ball is only makes contact where the seat ring aligns with the port of the ball. A trunnion has a "pole", for lack of a better word, coming out of the bottom of the ball and fitting into the casting.
Attached is a link to a pdf drawing of a floating ball valve, many years in the business and no one has heard of a pad support ball valve.