The photo is held by the Library of Congress and is available on their web site in glorious 10MB resolution. Their title for the photo is: "President-elect Wilson and President Taft, standing side by side, laughing, at the White House, prior to Wilson's inauguration ceremonies, March 4, 1913." Wilson had not yet taken the oath of office, so he was still the President-elect.
(The photographer snapped the picture just after Wilson had made a comment about a young woman nearby. The full picture shows Taft laughing uproariously, as he was wont to do.)