Newton's Third Law

Newton's third law: when body A pushes on body B, body B pushes back on A with a force of the same size in the opposite direction.

$$\vec{F}_{A \to B} = -\vec{F}_{B \to A}$$

Same force, different masses: the $40\ \mathrm{kg}$ cart gets the larger acceleration.

The two forces act on different bodies, so they never cancel each other. They can still cause different accelerations, because each body has its own mass.

Two skaters push apart. If the $30\ \mathrm{N}$ push gives a $60\ \mathrm{kg}$ skater $a = 30/60 = 0.5\ \mathrm{m/s^2}$, the same $30\ \mathrm{N}$ on a $40\ \mathrm{kg}$ skater gives $30/40 = 0.75\ \mathrm{m/s^2}$ the other way.

Walking works the same way: your foot pushes the ground backward, and the ground pushes you forward.