Vessel and Countertop
These types of basins sit on top of a worktop or furniture ; the vessel basin tends to be more bowl-like with the tap sitting directly on the worktop or fixed to the wall behind. The worktop surface will generally be lower than a surface of a cabinet where the basin sits in or under a countertop so that the basin top sits approximately 830mm from the floor. The Countertop basin looks more like a standard basin but it needs a very flat base to sit on the worktop and usually has a tap ledge at the back so the mixer can fit onto the ceramic although no tap hole can sometimes be an option.
There are various different colour finishes and materials that the vessel basins can come in ranging from ceramic, steel, natural marble/stone, man-made soild surface (mineral resin), cast iron, copper & glass which can allow you to make a real statement.
One thing to look out for is if the basin has a overflow hole or not. If it does not have an overflow then there is a chance you could flood the room if the plug is in and the tap is left running (depending on the waste you pick as freeflow ones are available which do not allow the basin to fill with water).