I just purchased the pre-order SE from Steam. Their forums there had a similar question which was answered by a 1C employee.
The answer was that while the standard edition will include co-op multiplayer, only the special edition will include PvP multiplayer mode, in addition to the co-op and other maps not included as part of the standard version.
If that response is valid, short answer is Standard Edition = no PvP, Special Edition = PvP.
Also remember that those details are for launch. It's still possible that in the future, with some sort of patch/update, PvP maps might be made available for the standard edition. But people are getting those extra features by paying for it, and as far as I'm aware Steam only sells the special edition anyways (which is also so far the cheapest version too).
If you want PvP, buy the Special Edition from Steam, wait for a possible future update, or look elsewhere.
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