Well the thing with poetry is that it's much more about feelings, emotions, thoughts and beauty then literature. I mean generally speaking.
Of course you can have different styles ect. as Kieve suggested, but because poetry is more personal it can differ much more then literature form poet to poet.
What
I would suggest is:
Poetry:
-Gods (religion)
-Cultural
-PersonalGods (religion)
Poems written in some sort of classical form, with the attempt to educate, inform, praise or ode about a (or more) gods.
Example: A Religious poem from a Laanx worshiper would be about self-bettering, a Talad based religious poem could be about helping others ect. This sort of poems would most likely be written by priest or very devoted followers and may not be the best poems you'll ever read (In an art sense)
Cultural
Different forms of poem for different cultures. These poems are about general 'issues' like Love, Hope, Doom, Beauty, Pride, Honor ect. These are meant to be fancy as they say something about your culture thoughts of things like the above. There may be various forms within a culture though often they are quiet related. Also It's not uncommon for a poem of this (ehhmm.. ) class (?) to not follow the form exactly, the form may be streached and bend in a modest way to make the
poem 'fit'.
Example: A (I can't find the correct naming ATM, sorry) major of a city may ask for such a poem to be written about her/his glorious city.
Personal 
Mostly based on feelings, emotions, thoughts and other things concerning the poet. she/he may choose the from themselves, they can use various like the ones for god poems or the ones for cultural poems but they may also choose to make a hybrid or neglect any from.
Expression on the individual poet should be the center, therefor it's unlikely these poems are being published by authorities or temples. The poet are going to have to publish and sell them their selves.
Examples here (<--clickie) or
here (<--clickie) if the server fails
Suggesting done
