Random terminology question: While I was aware of the term "Reef knot", that knot is commonly, almost exclusively, called a "Square knot" in my (midwestern American) dialect of English. Is this a British thing?
No. "reef knot" is a sailor's term. "square knot" is actually an overhand knot tied in the end of a line. "reef knot" (properly a "bend"), is the knot used to reef sails. The common shoe-lace bow is a "double bow reef knot" or "double slippery reef knot". Reef, bowline, and figure-eight are the three knots you must be able to tie behind your back to pass a basic sailing class.
I will reiterate though, that the reef knot is called a square knot where I come from. Misnomer? I guess, that's what everyone calls it, an overhand stop knot is an overhand or just a "knot" actually.