Probably the latter Matt - there's nothing unusual about experiencing soreness after your first few WODs! Your body is not used to performing the sort of work that the WOD requires, it'll take a while to adapt. Maybe you should consider "coasting" through a WOD or two if the stiffness is excessive.
EDIT: Just to expand on that last point a little, very few people are able to go "all out" on each and every WOD - there's no shame in holding back every now and then. Listen to your body; if you are sore, it might be an idea to cut the volume or intensity and use the WOD as active recovery. As a beginner, this is especially important - many a person has crashed and burned by trying to do too much, too soon.