Great question.
Bullets are resigned to do different things depending on their intended use.
For instance in hunting, a projectile will generally be designed to deform/expand quickly on impact with the intention to impart more energy to the target and do more damage which ultimately dispatches the animal more rapidly (and humanely). The different tips determines how much deformation and at what velocities the projectile deforms.
Similarly, in the military rounds are designed to do various things. The jacketed hollow point, for instance, is designed to deform/expand rapidly which makes it more effective and also helps reduce over-penetration, meaning the projectile is more likely to remain inside the target. It's no different to tank (and anti-tank) rounds having different tips and purposes.
In the case of the polymer tip you see here, it's generally done to make the tip (called the meplat) more uniform which improved ballistic coefficient. (BC); the better uniformity permits their flight is more predictable from one to the next.
In target shooting there's a projectile called a wad cutter, a flat-fronted projectile designed specifically to shoot at paper in target shooting on the range. It cuts a more precise hole permitting easier scoring in competitions. I've only ever shot them once or twice.
Projectiles are a science and a lot of research goes into developing them and tip design is one area of focus. I could write a book (several I guess) and still leave things out so my examples above are not very comprehensive. Essentially though, different tips aid in flight and knockdown characteristics depending on their intended use.
Thanks for your great question.