Improved Divine Smite Differentiation

Improved Divine Smite (PHB, p. 85) says in part:

… Whenever you hit a creature with a melee weapon, the creature takes an extra 1d8 radiant damage. If you also use your Divine Smite with an attack, you add this damage to the extra damage of your Divine Smite

Emphasis to show the part I’m focusing on.

So it was my understanding that Improved Divine Smite deals an extra 1d8 Radiant damage whenever I swing on a creature with a Melee weapon and hit them, no matter what else I’m adding to the weapon attack (such as Searing Smite, Divine Smite, poison I put on my sword before combat, etc). This definition makes a purpose of differentiating what happens if I also use Divine Smite with my attack.

I am more than likely confused or reading too far into the definition but I’d like to know why the book is making such a differentiation. What is it saying? That if I make a weapon attack without Divine Smite, the extra (non magical?) 1d8 radiant is added to the weapon damage, but if I do include a Divine Smite on the end, then the extra (now magical?) 1d8 radiant is added to the smite damage instead?

Does that change anything at all? Is this differentiation important to some sort of tactic or resistance I’m not considering?