Well, sort of.
Back when I worked at Atlantic Media, I explored the nature of the @BarackObama Twitter account. The way it works is this: After the 2012 campaign, Barack Obama and his allies formed Organizing For Action, a non-profit organization that was intended to carry on the grass-roots work of Obama for America, the 2012 campaign. In order to get people involved, OFA (which from here on out will be short for Organizing For Action) rented the social media accounts that were -- and still are -- owned by the Obama campaign. So @BarackObama, as its Twitter description indicates, is the voice not of Obama himself but of OFA. In fact, I was told that Barack Obama didn't have any say in the @BarackObama tweets. But as of writing (as of writing as of writing), the OFA account still tantalizes with the idea that Obama himself might occasionally tweet from the account:
The last time he did so appears to have been January 21, 2013 -- the day after he was inaugurated for the second time.
So what's the deal? Why is there an @POTUS account and an @BarackObama account, and, for that matter, an @WhiteHouse account?
The simple explanation is that "Barack Obama" on Twitter is much more appealing to follow and retweet than @OFA, which has only 305,324 followers (as of writing). Just as Random Anonymous Twitter Jokester is not going to have as much appeal as someone who is pretending to be Chris Rock, OFA's outreach efforts have a lot more spread when they come from the apparent mouth of the president. Sure, the bio says that it's OFA and that maybe Obama dips his toes into their stream on occasion, but who reads Twitter bios before retweeting? (Zero people.)
Now there's @POTUS, which will presumably become like the social media crown for whoever becomes the next president. Obama will probably shift back to @BarackObama, and give up @POTUS to @HillaryClinton or @RandPaul or @JebBush or @ScottWalker or whoever. (At time of writing, the 2016 election has not been settled.) (And, update: The account will indeed go to whoever wins.)
Will this reduce the clout/"engagement" from OFA's @BarackObama? Nope. Plenty of people will still assume that @BarackObama is Barack Obama and share @OFA's #content accordingly. Which Barack Obama is fine with, of course, since the whole point is to bolster his agenda.
So, to summarize:
Barack Obama is @POTUS.
OFA is @BarackObama.
The White House communications team is @WhiteHouse.
At least, at the time of writing.
Update: Barack Obama welcomes ... himself (?) to Twitter.
Well, that's unexpected. @POTUS (and the White House) says @POTUS is Obama. But @BarackObama (that is, OFA) would like to maintain the illusion that its account is also Barack Obama. So @POTUS becomes "the official government account of the President of the United States." Here's how @POTUS describes himself:
Unless "dad" and "husband" are official government positions, OFA is being rather deceptive. @POTUS is Barack Obama; @BarackObama is not.