At the peak its velocity (change in position) is zero because, as you said, it's not moving. Its acceleration (change in velocity) is nonzero because the velocity is still changing (it's only zero for an instant).

Crash course in calculus. :p:

Everything on earth is being pulled to the center of the earth same as a ball in transition from rising to falling so why isn’t everything at rest considered to have nonzero acceleration?

When forces aren't balanced, something is or is about to accelerate. When forces are balanced, no acceleration occurs.

The surface of the earth exerts a force upward that balances out gravity. No such force acts on a ball in midair that is about to plunge downward.

Newton's second law basically.

EDIT: Should we move this to the spam thread or something so it doesn't clog this thread up?

Like I'm basically asking if it's a difference in "philosophy" or if there's a measurable difference in equations. Like, is a thing that's not moving in mid-air because it's reached its zenith mathematically different from something that is sitting still simply because of gravity and air pressure that are working against each other but keeping said thing still?

I don't think anyone is worried about clogging the Your Day thread.

Yeah, there's a difference in equations. Calculus was invented basically for this question. You need an "open interval" (which can be arbitrarily small) of time around a given point to discuss instantaneous rate of change, and the difference comes down to the behaviour of the object in that open interval as it approaches the point you're interested in. In the case of the ball in mid-air, its motion changes immediately before and after the point in time at which its velocity is zero; the ball on the ground doesn't move at all.

Sorry I'm not explaining this very well, it's hard without math.

I think that’s a great question because it gets into why is there a different term for something just because the amount of time in that situation is negligible from a human perspective.

But the way we understand time philosophically does seem to influence the way physicists describe the phenomenon.

Time is what a clock measures.