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
B1Liège 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
A2Bouchon 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.