Accessory cord isn't used as a "climbing rope" in the sense that it is the rope connected to your harness that protects you from falls. It is usually thinner and comes in smaller length.

Here is a link to some accessory cord on amazon.com (you can get it at most climbing websites too).

Its advantages over paracord are that you can hang on safely (it is used in climbing for building anchors among other things where human weight is involved) however it is bulkier and more expensive, but not prohibitively expensive compared to a full on climbing rope.