I have to admit I did not know there was actually a word to describe the plastic or metal tip on the end of a shoelace, but there is and it’s called an Aglet.
The word “aglet” (or “aiglet”) comes from Old French “aguillette”, which is the diminutive of “aguille”, meaning, “needle”. OK it might be overkill but if you find this sort of thing interesting, I encourage you to check out Ian’s Shoelace Site where he lists 8 ways to repair your aglets.
These are aglets from, Aubercy, Church’s, Corthay, EG, GG, Weston see if you can put them in order from top to bottom. I will post the answer tomorrow.
Click on the image for a larger view.