Cert you might want to edit the whip words, because using shaft instead of stick can be confusing in a discussion about shaft length of a vehicle!
I was always taught it was whip stick and lash, with the bow between them on older whips. As with all horse related terminology, the names used can depend on local terms, who you learned from. At times it is like speaking two languages on the same topic, in trying to be specific! Probably why some parts have a double name, like tug loops, short tugs and long tugs on hames. All are tugs, but without the second part name, you have no clue which tugs they are.
We seem to like drop lash, long stick whips best. For us, they reach the horse well, may be able to touch them easier that short lashed whips. It does take practice to be able to touch exactly where you plan, to get the result you want. We add lash length to a regular long stick driving whip for ground driving and long lining. You want to be able to touch that horse anywhere on the circle or as you follow them. We never walk directly behind when ground driving, you can’t see what the horse is doing with their head and how much the reins are affecting their mouth. Off to one side works much better for us, especially with tall horses. The inexpensive black and white driving whips are pretty light, much easier to use for long times than the labeled “lunge whips” that are top heavy, have way too short of a lash to EVER reach the horse out on the lines, If you can’t touch horse with the whip lash out there, he has no clue you are not happy, can ignore you easily. Have to say yelling is not really helpful then.
If you plan to compete, check the ADS Rule Book for the correct distance allowed between horse rump and vehicle. It is listed for CDEs, not sure about Pleasure Driving section. Some folks got called out on it at Safety check at a CDE we attended. Way too close to the horse. They had to change their setting or could not continue to Dressage.