How free climbing compares to other styles of climbing is well explained in the question Bouldering vs aid climbing vs free climbing vs free solo climbing and more specifics are given in What does it mean to free a climbing route?. A recent answer to the question What is a “sling belay?” mentioned that such belays are considered "aid" in big-walling and makes an ascent non-free. First, I do not yet get the reasoning on how this is aid, for me it is just belaying which is fine. In general:
What specific rules like the one mentioned are there, that make an ascent non-free?
As this is often not uniform in area and time, any elaboration on where and when certain rules apply are appreciated.
This is not really relevant to a casual climber (as long as I do not put any force on the belay chain, for me I am free), but records and first ascent play an important role in professional climbing. Especially nowadays with more and more sponsorship involved, "regulation" and comparability are needed and I would like to understand the current "state of the art" of free climbing.