Gatto vs. felino
While both gatto and felino relate to cats, they are not interchangeable. Gatto is the specific, common word for a domestic cat, whereas felino is a broader, more scientific term for any member of the cat family.
Gatto
A1This is the standard and most common word for a domestic cat (Felis catus), the kind you would have as a pet. You use gatto in everyday conversations.
Il mio gatto dorme sempre sul divano.
(My cat always sleeps on the couch.)
Ho visto un gatto nero attraversare la strada.
(I saw a black cat cross the street.)
La ciotola del gatto è vuota, ha bisogno di cibo.
(The cat's bowl is empty, it needs food.)
Ci sono molti gatti randagi in questo quartiere.
(There are many stray cats in this neighborhood.)
Mia nonna ha un gatto persiano molto affettuoso.
(My grandmother has a very affectionate Persian cat.)
Felino
B1This term refers to any animal in the cat family (Felidae). It includes domestic cats but also lions, tigers, panthers, and cheetahs. It's often used in a scientific, zoological, or formal context. It can also be used as an adjective to describe cat-like qualities.
La tigre è il più grande felino esistente.
(The tiger is the largest existing feline.)
Il documentario mostrava il comportamento di caccia di un grande felino.
(The documentary showed the hunting behavior of a big feline.)
Si muove con una grazia felina.
(She moves with a feline grace.)
Il veterinario è uno specialista in malattie dei felini.
(The veterinarian is a specialist in feline diseases.)
Lo sguardo di quel felino nella giungla era intenso.
(The gaze of that feline in the jungle was intense.)
Summary
In short, use gatto when you are talking about a house cat in a daily context. Use felino when referring to the entire cat family (including wild ones like lions and tigers), or when you want to sound more scientific or describe a cat-like characteristic. Every gatto is a felino, but not every felino is a gatto.