Cima vs. picco vs. vetta

The Italian words 'cima', 'picco', and 'vetta' all refer to the top of a mountain, but they have subtle differences in usage and connotation.

Cima

'Cima' is a general term for the top or summit of something, not necessarily just mountains. It can also refer to the highest point of other objects or concepts.
Abbiamo raggiunto la cima della montagna dopo ore di arrampicata.
(We reached the summit of the mountain after hours of climbing.)
La cima dell'albero era coperta di neve.
(The top of the tree was covered in snow.)
È arrivato alla cima della sua carriera.
(He reached the peak of his career.)

Picco

'Picco' specifically refers to a sharp, pointed peak, often used for mountains with a distinctive pointed shape. It can also be used metaphorically to indicate the highest point or maximum level of something.
Il picco del Monte Cervino è uno dei più famosi delle Alpi.
(The peak of the Matterhorn is one of the most famous in the Alps.)
L'azienda ha raggiunto il picco delle vendite durante le festività.
(The company reached its peak sales during the holidays.)
Il picco di febbre è arrivato durante la notte.
(The fever peaked during the night.)

Vetta

'Vetta' is similar to 'cima' but is more commonly used specifically for mountain tops. It often implies a sense of achievement or the ultimate goal of a climb.
Gli alpinisti hanno conquistato la vetta dell'Everest.
(The mountaineers conquered the summit of Everest.)
Dalla vetta si godeva di una vista spettacolare.
(From the summit, there was a spectacular view.)
Raggiungere la vetta richiede preparazione e determinazione.
(Reaching the summit requires preparation and determination.)

Summary

While 'cima' is a versatile term for any top or summit, 'picco' emphasizes a sharp, pointed peak, and 'vetta' is mostly used for mountain summits with a connotation of achievement. 'Cima' and 'vetta' can sometimes be interchangeable for mountain tops, but 'picco' is more specific to pointy peaks and metaphorical highs.