The various summon types listed are the result of DMM aigis having so many premium units that they decided to break things into smaller pools so players have a chance of getting what they are rolling for. I'm not certain of the specifics as I don't play on DMM, but premium is the standard summoning, which I think they removed old units from, Revival is a summoning pool of older units that are no longer in premium, pickup is a summon pool with only a few platinums and blacks selected around a theme, imperial is limited to imperial units (a large category relating to some abilities and the story of later events). I would suspect that farewell might be a gacha for units that are leaving the normal premium pool.