Constructive & Helpful!
I asked them if the coat is different but they all said it's the same David's Coat but theirs just has that white trim at the bottom for some reason.
I got half of your answer, it's a bug/feature.
It's something weird that happens with Coat Armors (like David's coat, Santa Armor, Icelorn Mage Robes etc. basically any armor that has those sort of features) and certain boots, I think the criteria is that the boots need to reach a certain height just above the kneecap, or something like that for this to happen.
I screenshotted all the boots I could find and equip on my character/preview ingame, with David's Coat equipped. The Pebblar Boots in the Livingstone Craft shop will cause the same effect as shown with the Beta Berserker boosts, just with it's own green color. The ShadowSlayer E boots will also cause a VERY slightly different colored effect from the ShadowSlayer R example.
So if you wanted a white trim at the bottom, you would need to find the right boots, possibly the Frostlorn Rogue Boots, I don't have those to check right now.