The "with pads" thing is something you get if you played football for a number of years.
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When you first play tackle football, everything you wear seems like an obstacle. The 4-5 lb helmet on your head feels heavy. The facemask is in the way of your vision, the shoulder pads restrict your arm movements, etc. Even the knee pads drooping if your have ill-fitting pants slow you down.
As you play more and more, you get used to all of it, and some get used to it more or better than others. I knew guys in HS who still tilted their head back to look out below their facemasks. They never got comfortable with it.
So the guys who seem to "play fast" with pads on are simply the ones most comfortable out there. Their facemask no longer affects their vision, or perceived vision. They're used to the mobility restrictions and have had plenty of opportunities to work around it with confidence. They're the ones sure to get the right pants/pads/etc so they feel fast, and it's no longer a concern.