Soaps with a higher hardness tend to be able to take a polish better than a soft oil recipe.
Salt bars and brine soaps tend to be less shiny, and beeswax soaps more shiny, so as jcandleattic says, additives make a difference.
Some oils naturally add sheen (rice bran oil is one that springs to mind).
Gelled soaps tend to be more shiny than ungelled soaps.
Polishing soap can be done with a cloth or a gloved finger, and can make even an ungelled soap surface take on a sheen.
Dipping the soap in water (and perhaps a quick rub over the face to smooth it), immediately after the cut, can leave a shiny face on the cured soap.