Gilet vs. cardigan
In French, both gilet and cardigan can refer to a cardigan, but they have different scopes. The word gilet is a highly versatile term that can refer to a cardigan, a waistcoat, or various types of vests, while cardigan refers specifically and exclusively to a knitted sweater with sleeves that opens at the front.
Gilet
The word gilet is a broad, everyday term used for a garment worn over a shirt or top that opens in the front. It can refer to a knitted cardigan, a formal suit waistcoat, a casual sleeveless vest, or specialized safety gear like a life jacket or high-visibility vest.
Il a enfilé un gilet en laine car il faisait froid.
(He put on a wool cardigan because it was cold.)
Le marié portait un gilet élégant sous sa veste.
(The groom wore an elegant waistcoat under his jacket.)
Tu dois mettre un gilet de sauvetage sur le bateau.
(You must put on a life jacket on the boat.)
Tous les manifestants ont mis un gilet jaune.
(All the protesters put on a yellow vest.)
Le policier a survécu grâce à son gilet pare-balles.
(The police officer survived thanks to his bulletproof vest.)
Elle a acheté un gilet sans manches pour l'automne.
(She bought a sleeveless vest for the autumn.)
Cardigan
The word cardigan specifically means a knitted garment with long sleeves that fastens at the front with buttons or a zipper. It is a direct equivalent to the English word cardigan and represents just one specific type of gilet.
Elle tricote un cardigan rouge pour sa petite fille.
(She is knitting a red cardigan for her granddaughter.)
Il a boutonné son cardigan jusqu'en haut.
(He buttoned his cardigan all the way to the top.)
Ce cardigan en cachemire est très doux.
(This cashmere cardigan is very soft.)
Je préfère porter un cardigan plutôt qu'un pull à col roulé.
(I prefer to wear a cardigan rather than a turtleneck sweater.)
Le grand-père était assis dans son fauteuil avec un vieux cardigan.
(The grandfather was sitting in his armchair wearing an old cardigan.)
Summary
To summarize, use cardigan when you want to refer specifically to a knitted, long-sleeved sweater that buttons or zips in the front. Use gilet as a more common, everyday word for a cardigan, but keep in mind that a gilet can also be a waistcoat, a sleeveless vest, or safety gear. In fashion terminology, every cardigan is a gilet, but not every gilet is a cardigan.