Sous-vide - What does circulation accomplish?
Since temperature control is so vital to sous vide cooking, the circulation serves to make sure that all of the water is moving and of an even temperature. If you just had a heating element submerged without a circulator, you would get some convection currents, but there would be hot and cold spots in your water bath. If these differences were even just a few degrees, you could end up with proteins not hitting their coagulation temperatures, connective tissues not softening, pectin not broken down, etc. All in all, it would defeat the purpose of this cooking method!

As for the differentiation between "circulators" and "water ovens", there may not be one. Frequently the actual thermal unit and pump is referred to as the "circulator" and the whole assembly with a vessel and water is referred to as the "oven", but I'd check the specs of each model to see whether it has all the parts you're looking for.