As squeeze stated, driving lights/lamps and running lights/lamps, are (were) the lights/lamps used on a running/rolling vehicle. Marker lights/lamps were additional light/lamps.
To simply state and understand the purpose of Parking Lamps/Lights, slowly say the words out load and consider their meaning: start with "Parking".
In many states, parking lamps were not allowed to be on unless the vehicle was on/near the side of the road and was not moving.
It was also illegal in many states to be driving with only parking lamps on (perhaps because they are parking lamps and you were not parking).
And, in some states it was illegal to be parking on the side of a road with the driving lamps on (blinding and confusing on-confusing drivers).