Each of these pairs of words has the same relationship. A is a specific item, B is a category it belongs to. A is a countable noun, B is an uncountable noun.

Poem, poetry. 

Book, literature.

Painting, art.

Symphony, music.

Play, drama.

Horse, livestock.

Raindrop, water.

Grain, sand.

I like Robert Frost's poetry. Here is one of his poems:

Fire and Ice

Some say the world will end in fire, 

Some say in ice. 

From what I’ve tasted of desire 

I hold with those who favor fire. 

But if it had to perish twice, 

I think I know enough of hate 

To say that for destruction ice 

Is also great 

And would suffice.

I write a poem, I write poems, I wrote a poem about you yesterday.

A poem is a countable noun.

I write poetry

I love poetry

I love reading poetry.

From where we get the phrase, "poetic justice"

Poetry is more of an abstract idea, as in, 

"This piece of steak is simply poetry."

Fabricio, no, people who write poems are called poets.