Cuillère vs. cuiller
The French words cuillère and cuiller both refer to the exact same utensil, meaning a spoon. The difference between them lies entirely in their spelling and historical evolution, rather than their meaning or pronunciation, as both words are pronounced the exact same way.
Cuillère
The word cuillère is the modern and most common spelling used in everyday French to describe a spoon. It is the preferred spelling in contemporary dictionaries, everyday life, and modern writing because its spelling perfectly matches its phonetic pronunciation.
Je mange ma soupe avec une cuillère.
(I eat my soup with a spoon.)
Peux-tu me passer une petite cuillère pour mon café ?
(Can you pass me a small spoon for my coffee?)
Il a acheté un bel ensemble de cuillères en argent pour le mariage.
(He bought a beautiful set of silver spoons for the wedding.)
La recette demande d'ajouter une cuillère à soupe de sucre.
(The recipe asks to add a tablespoon of sugar.)
Le bébé a laissé tomber sa cuillère sur le sol de la cuisine.
(The baby dropped his spoon on the kitchen floor.)
Elle a remué la sauce tomate avec une cuillère en bois.
(She stirred the tomato sauce with a wooden spoon.)
Cuiller
The word cuiller is the traditional, older spelling for a spoon. Although the absence of the accent and final letter makes it look like an infinitive verb, it sounds exactly like the modern spelling, and it is mostly found in older literature, classic recipes, or used by linguistic purists.
Le poète a décrit une cuiller d'argent posée sur la nappe.
(The poet described a silver spoon resting on the tablecloth.)
Dans ce vieux livre de cuisine, on parle d'une cuiller à pot.
(In this old cookbook, they speak of a ladle.)
Il faut manier cette antique cuiller avec une grande délicatesse.
(One must handle this antique spoon with great delicacy.)
L'académicien préfère écrire le mot cuiller dans ses correspondances officielles.
(The academician prefers to write the word spoon in his official correspondence.)
Ma grand-mère gardait toujours une cuiller en bois près de la gazinière.
(My grandmother always kept a wooden spoon near the stove.)
Le manuel de savoir-vivre explique qu'une cuiller à moka est toute petite.
(The etiquette manual explains that a mocha spoon is very small.)
Summary
In summary, cuillère and cuiller are simply two different spellings of the exact same word. You should confidently use cuillère for all modern, everyday French writing, while recognizing cuiller as a perfectly correct, albeit old-fashioned, alternative that frequently appears in classic literature and traditional texts.