Vanity basins are used in conjunction with a stand alone bathroom vanity unit, a wash stand or with built in bathroom furniture.
Standard vanity basins are fitted into the top of a wash stand or freestanding bathroom vanity unit. These full depth storage units can hold a large amount of bathroom clutter but can eat up floor space and appear to "fill" a small bathroom.
A wash stand is an open design so it is not as imposing in a small bathroom, but it does take up the same amount of floor space as a vanity unit. Being open also means that a wash stand will not hide all of the clutter that tends to accumulate in a bathroom. Supply pipes and waste pipes might also be visible through the open stucture.
Semi-recessed vanity basins are designed to protrude from built-in bathroom furniture. The units that these basins fit into tend to be around half the depth of the basin so they are slimmer and neater, but as a result they have reduced storage capacity.
We have more details on vanity units and cupboards in our bathroom storage section