The first is a butchers steel, these were traditionally just a plain smooth steel rod which were used to repair the edge, shoving a knife through a joint tends

The first is a butchers steel, these were traditionally just a plain smooth steel rod which were used to repair the edge, shoving a knife through a joint tends to bend the very fine edge of the blade leaving what seems like a very dull spot. Essentially a heavy duty strop that would bend the edge back straight. These days they make them with abrasives embedded in the surface and are used to put a micro bevel on the knife, useful for the working chef but the home cook would be better off just sharpening the knife once or twice a month. A whetstone is just a synonym for sharpening stone. The oil helps keep the removed particles of steel from getting embedded in the stone and clogging it. Water or oil is used with most types of sharpening stones for this purpose.