Assuming no air resistance, all projectiles have

All projectile have parabolic motion and same vertical acceleration.

In fact, the motion of a projectile can be resolved separately in two directions: horizontal and vertical.

In the horizontal direction, the projectile moves by uniform motion with constant speed (because there are no forces acting in this direction).

In the vertical direction, the projectile has a uniformly accelerated motion, with constant acceleration (acceleration of gravity) downward.

The resultant motion of these two separate motions is a parabolic motion.