Soldering irons come in a variety of wattages but are basically all similar shapes. Soldering irons consist of an outlet plug, a grip, the wand and the tip. The soldering iron is held by the grip and the wand is the metal extension leading to the tip. The tip can be changed.
Stand alone soldering irons plug directly into an electrical outlet and then heat up to a certain temperature. The tip temperature is usually based on the wattage of the soldering iron.
Soldering stations consist of a base that plugs into an electrical outlet. The soldering iron is then plugged into the base. There is an on/off switch and sometimes a holder for the soldering iron. The soldering station base allows you to control the temperature of the soldering iron by turning a knob or dial. Some stations allow you to lock in a temperature so it isn't accidentally changed when soldering
The main difference between a stand alone soldering iron and a soldering station is the ability to control the temperature. This is important because some components you may solder could be heat sensitive.