Poema vs. poesia
In Italian, the words poema and poesia both relate to the world of poetry, but they are not interchangeable. They refer to different concepts, one being a specific literary form and the other being a much broader term.
Poema
B2A poema refers to a specific type of literary work: a long, narrative composition, often with a complex structure and heroic, mythological, or epic themes. Think of it as an epic poem or a saga in verse. It is a countable noun for a single, extensive piece of work.
La Divina Commedia di Dante è il più grande poema della letteratura italiana.
(Dante's Divine Comedy is the greatest poem in Italian literature.)
Il mio professore di lettere ci ha assegnato la lettura di un poema cavalleresco.
(My literature professor assigned us the reading of a chivalric poem.)
Scrivere un poema richiede anni di dedizione e studio.
(Writing a long narrative poem requires years of dedication and study.)
L'Iliade è un poema che narra le vicende della guerra di Troia.
(The Iliad is a poem that narrates the events of the Trojan War.)
Poesia
B1A poesia is a much more versatile and common word with three main meanings. It can refer to 1) The art of poetry in general, as a literary genre. 2) A single, individual poem, which is typically shorter and more lyrical than a poema. 3) The abstract poetic quality, beauty, or emotional resonance of something.
Mi piace leggere la poesia moderna.
(I like to read modern poetry. (Here it refers to the art form).)
Ho scritto una breve poesia per mia madre.
(I wrote a short poem for my mother. (Here it refers to a single, short piece).)
A scuola abbiamo imparato a memoria una poesia di Giacomo Leopardi.
(At school we learned a poem by Giacomo Leopardi by heart. (A single composition).)
C'è poesia nel silenzio della neve che cade.
(There is poetry in the silence of the falling snow. (The abstract, beautiful quality).)
Il suo modo di parlare è pura poesia.
(The way he speaks is pure poetry. (An abstract, beautiful quality).)
Summary
In short, the key difference lies in scope and nature. Use poema for a single, long, narrative, and often epic work like The Odyssey. Use poesia more broadly for the art of poetry itself, for a single (usually shorter and lyrical) poem, or for the poetic beauty found in a moment, a place, or an action. You can have many examples of poesia within a collection, but a poema is a single, monumental work.