Two bumper cars slam into each other, and both riders feel the jolt. Plenty of forces act during that moment: each car on the other, the floor's friction on each car, the Earth's gravity on everything. One kind of force stays inside the chosen system; the other reaches across its boundary.
Take the two bumper cars as the system. Every force in the scene now answers one question: are both objects in the interaction inside the system?
The system is the two bumper cars. A dashed boundary is drawn around the pair; the floor and the Earth sit outside it.
First force: during the collision, car A exerts a force on car B. Both A and B are inside the boundary. A force between two objects that are both inside the system is called an internal force.
Next force: the floor's friction on car A. The floor is outside the boundary; car A is inside. A force between an object inside the system and an object outside it is called an external force.
Next force: the Earth's gravity on car B. The Earth is outside the boundary. So the Earth's gravity on car B is an external force.
Last force: the force car B exerts back on car A during the collision. B and A are both inside. That force is internal.
Now a new choice on the same crash: let the system be car A alone. The force from car B on car A now crosses the boundary, because car B is outside. The same force that was internal for the pair is external for car A alone. Internal or external is a fact about the force and the chosen system together.
Two rail cars couple on a track. The system is the two rail cars. Sort these two forces: the coupling force of one car on the other, and the track's friction on the leading car.
The coupling force acts between the two rail cars. Both cars are inside the system, so the coupling force is internal.
The track's friction acts between the track and the leading car. The track is outside the system, so the friction is an external force.
The coupling force is internal; the track's friction is external.
The system is two shopping carts that collide in an aisle. Is the force of one cart on the other internal or external to the system?
The system is two sleds that collide on packed snow. Is the snow's friction on one sled internal or external to the system?
The system is a soccer ball and the goalpost it bounces off. Is the Earth's gravity on the ball internal or external to the system?
The system is two football players who collide. Is the force one player exerts on the other internal or external to the system?
The system is a train engine and the freight car it is coupled to. Is the force of the engine on the freight car, through the coupling, internal or external to the system?
The same engine and freight car, still the chosen system. As the pair rolls, the rails exert a force on the engine's wheels. Is the rails' force internal or external to the system?
The system is two ice skaters who collide. Which of these forces is internal to the system?
Two canoes bump on a lake. For which choice of system is the force of canoe 1 on canoe 2 an internal force?
Which test says a force is internal to a system?