Can you shed some light on this dust-shielding ferrule?

Question

I understand that the two parts at the top of the image are an improved ferrule. They rest against the lowermost cable rest — the one nearest to the rear derailleur.

Can you shed some light on these two parts?

For example:

1. Is there any preparation needed before using these two parts (grease, or lack thereof, etc)?
2. What are they called? Their name will help with searching for usage videos and documentation.

Answer 1

1. Applying a small dab of lightweight grease (such as Shimano's own SP41 cable grease) may help reduce friction and increase weather resistance, but if you only have thick bearing grease you're probably better off without it. Too much and/or too viscous of a grease may attract dirt and cause undesirable viscous drag.
2. I'm not too familiar with the one on the left, but the one on the right is a Shimano "Shift Outer cap with long tongue". Jagwire also makes a similar device called a "lined end cap" (thanks Weiwen!). Compared to normal ferrules, these are supposed to have better weather resistance and help smooth out what would be sharp bends in order to protect the cable.

Answer 2

(Follow-up to MaplePanda's answer)

Do not confuse the shift outer cap with long tongue (bottom of the first image below) with the outer cap with short tongue (top of the first image).

The shift outer cap with long tongue is used to weather-proof rear shifting by stopping sand/dust from entering the cable cover.

The outer cap with short tongue, as you see in an excerpt from a Shimano Dealer's Manual, is the end of the Bowden cable that sits against the brifter.

In addition to having a long or short tongue, another difference is that the outer cap with short tongue has a slant-cut short tongue and a notch that stops it from rotating, to ensure that the slant-cut tongue is properly positioned.