I was reading both of them, and if you had a hypothetical Barbarian Paladin multiclass, would the use of divine smite be prevented by raging? Unlike other smites, it says that it expends a spell slot, but isn't listed necessarily as a spell. It reads more like a special ability that just happens to cost a spell slot.
Divine Smite:
Starting at 2nd level, when you hit a creature with a melee weapon attack, you can expend one spell slot to deal radiant damage to the target, in addition to the weapon’s damage. The extra damage is 2d8 for a 1st-level spell slot, plus 1d8 for each spell level higher than 1st, to a maximum of 5d8. The damage increases by 1d8 if the target is an undead or a fiend.
Rage: (Relevant portion)
…If you are able to cast spells, you can’t cast them or concentrate on them while raging.
Best Answer
You can smite divinely while enraged.
There's no spell named divine smite; you're not casting a spell when you use that class feature. It's a feature triggered when you hit with a weapon attack.
This, by the way, is another way you know it's not casting a spell: you're (most-likely) taking the Attack action to make your melee weapon attack, rather than the Cast A Spell action. It's rare--and explicitly spelled-out circumstances--where you'd make an attack but end up casting a spell.