Well, if you look at the religions in dnd in a way that is vaguely resembling the real world catholic orders (and the cleric and paladin share an origin in those cultural whereabouts), it's relatively simple:
Cleric: he's a real priest. He takes all the vows, is fully ordained, is a part of the church's power chain/structure (i.e. could become bishop, or equivalent), and normally administers sacraments, sanctifies weddings, blesses the cattle, and so on. He's the guy that preaches in the temple.[*]
Paladin: he's a soldier. He's taken only some of the vows and cannot preach, or administer sacraments. He's a man of faith, but not a priest. Basically, it's modeled after the Teutonic Knight, or the Templar Knight. They took only some of the vows of the monastic orders, and were militant orders.
[*] and yeah, DnD's cleric is much more 'action oriented', what with all that mace swinging and kobold bashing, but let's say that in a world with so many deities and dangerous creatures you can expect a priest to take some interest in his personal safety while traveling through the heathens
