According to Merriam-Webster Dictionary, Poem is "a piece of writing that usually has figurative language and that is written in separate lines that often have a repeated rhythm and sometimes rhyme".
Shayari, as Wikipedia quotes, "In Urdu, poetry or Shaayaree, essentially comprises couplet, or Sher. The form ghazal is a collection of mulitiple ashaar - each of which should convey a complete thought without any reference to other shayari of the same ghazal. In fact, though belonging to the same ghazal, the different ashaar therein can have completely different meaning and tone relative to one another."
This means that Poem refers to all kinds of poetry in every language whereas Shayari is a form of poem written in Urdu.
