My reading is that a staff is a staff. Like daggers for sorcerers, holy blades for paladins and light and heavy blades for swordmages it can either be an implement or a weapon depending on how you use it.
I'd actually been wondering if a staff when used as an implement was 1H or 2H. Do you see anything in the rules that addresses the handedness of staffs when used as an implement. Clearly when you wield a staff as a weapon it is 2H.
I would say that a quarterstaff _can_ be used as an implement in place of an implement staff .. though if it isn't a magical quarterstaff it wouldn't provide any enhancement bonus. (My understanding is that there are +0 wands, orbs, rods, and holy symbols just like there are +0 (quarter)staffs.)
Holding a non-enchanted quarterstaff is enough, in my reading, to allow a staff wizard to activate his or her con mod based encounter defensive bonus. Just like holding a non-enchanted wand will allow a wand wizard to get a bonus to a single attack roll equal to their dex mod.
A staff (with a bonus or not) that is an implement can certainly be used to resoundingly pound foes skulls, and if the wielder had staff or simple melee proficiency then they'd get the +2 proficiency bonus when doing so.
That's my reading of the rules, anyway.