a First Press poster is a poster you receive with the first press of an album / single, for example SECRET, GUILTY or Mirrorcle World.
They are always text-less.
My guess is that promo-posters are posters that are made for just that: promotion. Their purpose is (I think) hanging around stores and malls in Japan :p They usually do have text and release dates on them, but not always I guess.
I consider First Press poster more as "official" posters, and promo posters as just really fun, nice posters to have!