In some contexts they mean the same, but differ syntactically...
I will always love you. I will love you forever. /not/ ?I will forever love you. 1
In other contexts there's a difference in that always usually means continuously, at all [relevant] times, whereas forever usually means for an infinite amount of time into the future. Thus...
He always catches the bus at 8am. /not/ *He forever catches the bus at 8am.
The universe may not last forever. /not/ ?The universe may not last always.
...where some people may find that last construction more acceptable than others.
Here's a useful summary of usages for always, only one or two of which overlap with forever.
1: The song I Will Forever Love You does exist, but it's nowhere near as well-known as I Will Always Love You, written and first recorded by Dolly Parton, massively popularised by the late Whitney Houston.
Literacy, pens, paper, the printing press.
A written culture has different restrictions than an oral culture dependant on ease of repetition from memory.
According to the University of Wisconsin Digital Collections Center:
Beowulf is the oldest narrative poem in the English language, embodying historical traditions that go back to actual events and personages in fifth- and sixth-century Scandinavia. During the long preliterate centuries when these traditions were transmitted in the form of oral poetry, they were combined with with a number of legendary and folktale elements (among these are Grendel and his mother, the dragon, and probably the hero Beowulf himself). The written text of the poem, as we have it today, took shape in England during the middle or late Anglo-Saxon period and survives in a single manuscript from around the year 1000.
An oral tradition requires stories to be easily memorised and stand repetition many, many times, and passed on to the next storyteller. A strong metre and fixed structure with helps, along with alliteration (also found in Beowulf) and isn't unique to English. For example, the Finnish national epic, the Kalevala, is based on sung oral tradition and has a fixed pattern of stresses, with much alliteration and parallelism (repeating the previous line with different words but meaning the same thing). In fact, the hero, "steady old Väinämöinen" (an almost always alliterative "vaka vanha Väinämöinen"), is himself a storytelling wizard who plays a zither and uses his song-words for magic.
Once people can read and write, they no longer have a need for the storyteller to recite a story from memory, they can read it themselves, or have someone read it to them from a text. Over time, this gives rise to more creative ways of expression.
For more, here's a paper (PDF) on Oral Tradition & Its Decline by Indira Bagchi.
Best Answer
To me poetry is a literary art. A poem is a piece of poetry.