Orodruin said:
All that you quoted was referring to the accelerated frame in which the car is at rest. In this frame, there is afictitious force acting on all objects, which is necessary for Newton's second law to hold. In an inertial frame there are no fictitious forces, it is as simple as that. The force accelerating the car is equal to its mass multiplied by its acceleration as per Newton's second law. There is also a force from the car on whatever object is pushing it and this force acts in the opposite direction and is a very real force, but it is not acting on the car (in the typical accelerating car, this is the friction force on the ground).
I am sorry, but even if you have read the wiki, it does not seem as if you have actually understood what it says.
Actually I think I understand the topic, but I am looking on it from broader perspective than others. I will explain it on example.
So we have accelerating car with driver. The car needs F=ma to accelerate and as m is calculated the weight of car including the weight of driver. Standard view is that the fictitious force is only acting on driver, not on car. And the fictitious force acting on driver is -ma, with m of driver, let's say 100 kg.
But let's have second example, where we have special the same driver driving a special light carbon bicycle weghting only 1 kg. So standard view is that to accelerate bicycle we need F=ma, where m is m of driver + m of bicycle. And the fictitious force acting on driver is -ma with m of driver 100 kg. But this time almost all F accelerating the bicycle is used to counter the -ma of fictitious force.
Lets have third example where the bicycle is so light, that we can ignore it. And we have F=ma with m of driver and -ma counter force which is fictitious / inertial force.
So what I am saying, that my definition is broader and doesn't use this ridiculous non inertial reference frame.
Just to repeat, how it is in reality:
There is only one fictitious/inertial force and this force is acting on accelerating object in opposite direction to direction of acceleration.
You will not be able to find example which is not covered by this easy definition, when we abstract from relativistic effects.