These people in the moderate groups, like 'Elks', in the outer orders, have no idea what they are really doing.

These groups are layered by degrees, from outer to inner, and the secrecy oaths are take as one is initiated into each inner layer.

As the layers get to the third order or beyond, I assume they all look like the same 'order', even though the outer rings may look different, to the point of innocuous social clubs.