So it detects a fast increase in the infer red energy within it's field of view...
More-or-less. It detects a sudden change in IR magnitrude OR a movement of a source of IR energy across its field of view (hence not very sensitive to IR sources moving directly towards or away from the sensor).
... and is saturated in daylight so can't detect any change. Is that how it works?
Not really. PIRs will usually work as well in bright daylight as in the dark, if one wants them to, since the IR sensor is minimally sensitive to visible light. However, in many/most applications, one does not want them to work during daylight - so there is a separate (visible light) photocell and an adjuster so that (if one wishes) one can set the PIR to only work when the (visible) light level is below the set level. Conversely, you can adjust it so that the PIR always works, regardless of the ambient visible light level.
So reversing in will not trigger it as car is not changing the energy it can detect, but coming in forward will as radiator is hot.
That will be part of it - although, as I have said, PIRs are at their least sensitive when a heat source is moving directly towards or away from the sensor.
This also explains why it seems more sensitive at night than during the day.
The ambient temp is going to be lower at night, so heat from radiator, bonnet or exhaust will have a greater differential from ambient, and therefore more likley to trigger the PIR.
So where there is an outside light which emits a narrow frequency of light say a blue LED then the device will not be triggered, but a tungsten lamp would trigger it?
As above, PIRs are not (or should not be) triggered by visible light. If the visible light is bright enough, it may inhibit the PIR action, depending upon how you have set the light sensitivity adjustment.
Do sodium lamps give off infer red energy?
I'm sure they will give off some (as does virtually any lamp) but I have no idea how much. However, since the light is (once on) of constant brightness and not moving, it should not trigger a PIR (except, conceivably, when the lamp first comes on).
Kind Regards, John