This is a stub … I hope to just add notes here when I come across things that inspire me to add more.
A circle can be draw in many ways, in some cases with symbols interwoven with the edges of the circle like in the ritual form of the LBRP. In some instances however it is simply draw as a simple circle. I believe this action is taken from Liber ABA into modern Wicca. It is also common that calling the quarters is considered part of setting up the circle.
In Ceremonial Magic the circle is primarily invokes as a power to keep harmful spirits out. For this reason symbols and divine names are often woven into the circle to invoke powers to protect the magician. Consider the representation of Dr John Dee summoning a ghost here where the circle surrounds and protects the summoners. Note the use of symbols in creating the circle.
In the American Wiccan practice I have come across a lot of references to the drawing of the circle being used for a different purpose. It is done to bring spiritual worlds and physical worlds together as if they are separate.
My own experience with American Wiccans is that they view it as creating a spiritual space where magic can happen, as if it can’t happen outside of that space. But it essentially is viewed as not only protective, but bringing the worlds together.
It is worth comparing this with the Trad craft ritual where they quickly open 4 roads going inward into the circle so it quickly becomes a gateway between the worlds.