I think the spiral vs. braided challah may be a function of your family and community. I was brought up that the spiral ("just rolled into rounds") challah was for Rosh Hashanah, and a Google search turned up over a dozen sites that agree with that.

OTOH, I've also seen people make braided round challah for Rosh Hashanah and spiral loaves for Sukkot (and for Shavuot, too). It seems to be highly variable, with the exception being that everyone agrees that Rosh Hashanah challah should be round (even if they disagree on whether or not it ought to be braided).