Both in a sense, the square tooth has a straight edge or squareness to it; whereas the round chisel tooth has a curvature to it. Also, the files are different; round file for the round chisel chain. And there are three popular files for hand filing square chisel chain, ie, triangular, bevel edge, and a "goofy" flat file. The latter file does not allow you to maintain a true square edge; but, it does allow you to file a square chisel chain to where its usable in the field. The quickest and best method of filing the square chisel chain is by machines designed to grind that particular type chain. And they are expensive.
My personal experience is a square chisel chain is fast in the cut, quickly dulled by dirt, etc, and "can" be hand filed, "IF" you have the tools and patience to learn how to do it. I'm a firewood cutter and have the square chisel chain on all my saws.
Some people buy the square chisel chain and then convert it to round chisel after using it a while. This can easily be done on a cheap grinder.