There is a lot to unpack here, but basically there are two different phenomena at play.
Namely kinetic energy or energy acquired by an object simply because it is moving (relatively to another object). If an bject of mass $m$ moves at a speed $v$, it’s kinetic energy $E$ is:
$$ E = m .v^2$$
So the energy carried by an object, owing to its it motion or speed $v$ increases with its mass but it increases much faster with its speed:
- An object $10$ times more massive ($m1 = 10m$) has ten times more kinetic energy with at a given speed than an object of mass $m$.
- An object which is $10$ times faster ($v1 = 2 v$) has a hundred times more energy than an object of mass $m$:
$$ T1 = m .v1^2 = m (v.10)^2 = m. v^2 100 = 100. T$$
This is why a bullet is more harmful than a stone: its lighter, but its faster.
When an object in motion hits another object, the object which is hit slows it down and gets thereby a part of the energy of the incoming object transferred in return.
If an object is heavy and/or moves fast, it will transfer a lot of energy to the object is hits.
It is said transfer of energy which will damage the object on the receiving end, because it will absorb it.
One could explain the same thing is terms of force as well (one can demonstrate that these two explanations are equivalent mathematically speaking).
In order to accelerate an object set it in motion or increase its speed, one has to apply a force to it.
In Newton’s terms acceleration ($a$), force ($f$) and mass ($m$) are related as follows:
$$ f = m a \tag 1$$
The same is true for deceleration (which technically is the same as acceleration, just with a reversed sign).
In other words, the stronger an object is decelerated, the more force it will exert on the object decelerating it, according to Newton’s law (1), above.
The second reason a bullet is potentially more harmful than a stone is: force per unit surface or pressure.
If an object exerts a pressure on another object, the larger the surface over which a given pressure is spread, the less energy it will be able to transfer energy on a precise location.
A bullet having the same mass and the same speed as a much larger rubber ball will do much more damage on impact, because its kinetic energy will be transferred onto a much smaller area. This is also why a knife or an axe have to be sharp to be effective (if not the force is spread (and hence it’s effect) over a large area).