What you're seeing
Two objects touch for a short time. While they touch, each one pushes on the other. The red arrows are those two forces. They are always the same size and point opposite ways. That is Newton's third law.
The blue arrows are the accelerations. The same force has a bigger effect on a smaller mass: a = F / m. That is Newton's second law.
When they stop touching, the force is gone, so the acceleration is gone too. Each object just keeps its speed. That is Newton's first law.
The panel below the picture shows it as Ma = F = mA. The big object gets a big M and a small a. The small object gets a small m and a big A. Letter sizes show how big each value is (on a squeezed scale, so the huge ones fit).
Things to try
Bug & car: before you press Start, predict which object feels the bigger force. Then pause during the impact (Space bar) and compare the red arrows.
Make the bug heavier with its slider. Watch the force stay equal while the accelerations get closer together.
Billiard balls have equal masses. What do you predict for the accelerations?
Skater & wall: the wall is attached to the whole Earth. Find the wall's acceleration in the panel.
What this leaves out
Real impact forces rise and fall. Here the force is held steady while the objects touch, so it is easy to compare.
No friction, no air resistance, no engine or brakes on the car. That is why things coast after contact.
Masses and contact times are round numbers chosen for illustration. Objects are not drawn to scale. The impact is shown in slow motion; before and after run at real speed.