So you're asking about two things, pressure difference across the radiator, and speed of airflow.
First, regarding pressure difference. The radiator core is a resistance to flow, and if there was no pressure difference across the core, there would be no airflow. And, the higher the pressure difference, the higher the flow. It is just the same as an electrical circuit with a resistor. If there is no voltage difference across the resistor, there will be no current flow, and the higher the voltage difference, the greater the current flow.
Second, regarding airflow speed. If we think of the airflow approaching the car, the more we can slow it, the higher the pressure. So the highest pressure recorded on a car is the stagnation pressure, where the airflow has been brought to a halt. In other words, flow speed is traded for pressure, or pressure is traded for flow speed. So if we can slow the speed of the airflow to zero (or nearly zero) in front of the radiator, we will have the highest pressure (good) and the lowest speed (good).
Now, as Scibor-Rylski explains, let's look at an idealised cooling system. We let the air in at high speed and then progressively slow it by using a diverging (ie increasing cross-sectional area) duct. Pressure rises as speed falls, until at the core, speed is low and pressure high. There is a pressure drop through the core, but now we have heat energy added to the air. We then use a converging duct to increase airflow speed and lose pressure, until at the exit duct we have the airflow speed matching (or even exceeding) the free stream speed. Then we smoothly add this exit air to the airflow around the car, thus creating little drag - or maybe, as was done in some WWII aircraft, even a little thrust.