I'm not sure what kind of climbing ropes they are exactly, but the ones I saw online (a bunch of them...) are usually twice as thick (10mm~) as most paracords (4mm~) yet the paracords claim to have twice as much load bearing! Why??? Does that make the paracords stronger?
Essentially para cord is stronger, but its less resilient.
Climbing ropes do not need to be strong - you die above about 10G (1000kg) force from internal injuries caused by your harness, a braking strain above this is pointless, even if the rope does not break in a fall that generates very high G forces, you die.
Anchors have a force, which if exceeded even for a very short time, will cause the anchor to pull out. Biners, slings and quick draws have a force that will cause them to fail (typically a few 10's of kN ) - above this they fail.
A climbing rope will stretch and absorb forces - reducing the very high, short time loads to a lower, longer time frame load - think wire vs rubber band. The maximum loading on the hardness and the anchors is reduced to a constant below the point that failures occur. Para cord has no stretch. The force was the para cord comes tight is applied to the system in one short instant.
Climbing ropes must also be able to resist cutting and chaffing causing them to weaken and break. As they are stretchy to absorb the shock loading, this chaffing can be quite significant. They can be cut by a rock landing on top of them, or being pulled tight over a sharp edge.
All of these issues are managed by the construction - The strength is provided by an inner core, and an other sheath that protects the core.
Para cord on the other hand is build to have no stretch, and has no need for protection from chaffing and cutting. Its very strong and very light. Its good for static loads where there is no chance of damage to the cord. Because of this, it can be made much smaller and lighter than climbing rope.
Climbing ropes are meant to hold falls, and to absorb the shock of the fall itself through stretching (they can stretch up to 30% of their length during a severe fall so to reduce the impact force on the climber).
There's no need for a climbing rope to hold more than it does, because any more force during a fall and the body of the falling climber would be injured to death nevertheless.
Paracord in turn does not need to stretch (actually, it's a bonus that it doesn't, for its usage) because it is not meant to hold a fall, but just a static (as in "non-falling") load.
Thus, the two kind of ropes are made with very different specifications. The non-stretching paracord can be much more resistant to static loads while being thinner because it does not have to adhere to the severe rock climbing specifications about dynamic (as in "falling") forces.