Road cycling shoes have one very specific feature… the sole is very stiff. As there is no need for any shock absorbency in a road shoe the sole is stiff so that as much of your energy goes into turning the pedals. Very early road shoes were made with wooden soles and if a cleat was needed it was nailed (tacked) to the sole.
Modern road shoes have soles made from composite materials, including carbon, and are both very stiff and light. Unlike a mountain bike shoe the cleat is not recessed into the sole so walking around in road shoes is a little cumbersome. To help with walking lots of road shoes have toe inserts and replaceable heel pads.
So expect a firm fit with a quality road shoe – and opt for a wider sized shoe if you find a standard one too narrow. Modern shoes use velcro and/or buckle mechanisms to keep them in place – again, the shoe is designed for optimum performance.