Clerics turns that into something that lasts
In short it not their abilities that set the two aparts but the roles they play in their religion. My view of paladins and what they are is heavily influenced by Elisabeth Moon in her Deed of Paksenarrion series.
Paraphrased From page 579 of the Trade Paperback the Dead of Paksenarrion.
Most think being a holy warrior means gaining vast arcane powers, that they would be nearly invincible against any foe. But truth is that while Paladin are skilled at fighting, that was the least of their abilities. A quest might involve no fighting at all, or a battle against beings no steel could pierce.To me this is most gamable summary of a DnD style paladin I ever read and the basis for how I referee them. It is the core of what went into the Majestic Wilderlands supplement not only for Paladins but Myrmidons as well.
Above all paladins show that courage is possible. It is easy enough to find reasons to give in to evil. War is ugly as many know. But we do not argue that war is better than peace; paladin are not that stupid. It is not peace when cruelty reigns, when stronger men steal from farmers and craftmen., when the child can be enslaved, or the old thrown out to starve, and no one lifts a hand. That is not peace: that is conquest and evil.
Paladins do not start quarrels in peaceful lands, never display their skills to earn applause. But we are the sword of good defending the helpless and teaching by our example that one person can dare greater force to break evil's grasp on the innocent. Sometimes that can be done without fighting, without killing, and that is best.
But some evil needs direct attack, and paladins must be able to do it, and lead others in battle. Wonder why paladins are so likable? It is important, we come to a town, perhaps, where nothing has gone right for a dozen years. Perhaps there is a temple there and sometimes there is not. The people are frightened, and they have lost trust in each other, in themselves. We may lead them into danger, some will be killed or wounded. Why should they trust us?
Because we are likable, and other people will follow us willingly. And that's why we are more likely to choose a popular adept as a candidate rather than the best fighters.
The Cleric job is work with a specific group, locale, or organization for his religion. Wisdom is required not just for common sense but also the willpower to endure the slow millstone of time that comes along with the job. A paladin will come through, lead the charge to break evil's grasp, and go off on his next quest. Then it become the Cleric's job to pick up the pieces and build something lasting in the name of his god.