The square knot is basic knot tied between two rope ends; the first half of it is much like the first half of the shoe's knot. You then repeat the first half, but swapping which end is on top. Like the shoelace knot, if you do it right, it stays inline (and remains symmetrical and pretty); if you do it wrong, it gets ugly.
Really (at least to me) this is because the shoelaces knot is a square knot; the "bunny ears" are simply added slipknots to make it easier to untie your shoe. But I've never seen the "standard" method taught to tie a square knot, likely because I've never seen the square knot taught with slip knots; those just being something you add if you want them.
Which is how I tie my shoes; I use what the article calls the "two loop knot"[1]. Two methods, same knot, though I always thought my way was the standard, not my dad's. Oh well.