Liège vs. bouchon
In French, the words 'liège' and 'bouchon' can both be translated to 'cork' in English, but they have different uses depending on the context.
Liège
'Liège' refers to the material 'cork' itself, which is derived from the bark of the cork oak tree.
Le tableau d'affichage était fait en liège.
(The bulletin board was made out of cork.)
Le liège est un matériau naturel et renouvelable.
(Cork is a natural and renewable material.)
Bouchon
'Bouchon' typically refers to a cork stopper, such as those used in wine bottles, or more broadly to any kind of stopper.
Il a retiré le bouchon de la bouteille de vin.
(He removed the cork from the wine bottle.)
Le bouchon de la baignoire ne fonctionnait pas.
(The bathtub stopper wasn't working.)
Nous avons rencontré un bouchon sur l'autoroute.
(We encountered a traffic jam on the highway.)
Summary
While 'liège' refers specifically to the material 'cork', typically used in making various products, 'bouchon' is used for cork stoppers (like those in bottles) and can also refer to stoppers or plugs in general. Moreover, 'bouchon' has an extended meaning of traffic jam in everyday language.