There are plenty of ways to make FETs. One way to distinguish them is lateral vs vertical:
Lateral MOSFET: current travels parallel to the plane of the semiconductor chip.
Vertical MOSFET: current travels through the flat semiconductor chip, from one side to the other side.
Take any wire, the thicker it is, the less resistance it'll have: resistance is inverse proportional to conductor cross section. Same thing happens with MOSFETs: in a vertical MOSFET, current travels from one side of the chip to the other, so the available cross section is close to the area of the chip.
In a lateral MOSFET, current travels across the chip, so the available cross section is limited by the thickness of the MOSFET, which is tiny. In other words, vertical MOSFETs allow lower RdsON, so they are popular in power switching applications.
Here's a cutaway view to illustrate (source):

There are many different types of discrete Vertical silicon MOSFETs, but they all have the drain on the bottom side of the chip. That's also the bottom side of the wafer. It is flat and there is only one contact there, whereas on the top side there's both source and gate. So it is practical to solder the chip on a metal tab, which then becomes the drain:
(pic source)

Soldering the chip on the copper tab gives very low thermal and electrical resistance, so usually the drain tab is also used for cooling.