These categories deserve elaborated details. Because they can do wonders in the right hands and might ruin your experience if it is not suited.
Farmhouse kitchens are long basin sinks that are designed to do heavy-duty work. They are made with incredibly durable materials like steel and cast iron. Don’t confuse them with utility sinks. But they are also called apron sinks.
Bar or prep kitchen sinks might be the most useful thing in the kitchen after the primary sink. Yes, it is not your primary sink, but rather a small sink beside the main kitchen sink. The low basin single bowl sink is mostly used for preparation work and is very busy during parties for drink making.
Corner sinks are designed to be installed in the corner of your kitchen counter. These might not be the norm but are very efficient in small kitchens, mostly because you rarely have to open the bottom of the sink. There are generally two bowls and a drainboard on the sink.
Drainboard kitchen sinks are simply those sinks that have a roughly textured space beside the sink basin, primarily to drain out all the excess water from the dishes. This is a convenient feature and available in both budget and premium sinks.