This question is a very philosophical one about the nature of history as a discipline. When I decided to study history, it was because at the time I would have answered this question simply with, "yes, isn't that great?" but in the process of actually studying it, my views have shifted a lot. My loose operating definitions are that the past is what happened, history is how we talk about it. In that sense, history is not so much a tidy story as it is us trying to draw conclusions about sometimes big questions like "Why did this happen" and "What does this mean?" and sometimes very focused questions like "So, what actually happened?" If you'll forgive a quick transgression of the twenty year rule, discussions about 9/11 would fall into the first category (we know what happened and understand a good deal about why it happened, continued discussion is largely focused on the implications it has had since) and discussions about Malaysian Airlines Flight 370 fall into the second (we have very little idea about how events actually transpired, and most discussion is focused around determining a sequence of events).
I'll draw on a slightly more historical example. There is a British historian by the name of David Irving. Irving is an incredibly gifted reader, speaker and translator of German, a resourceful researcher, and an expert on the Second World War and especially Hitler and the Third Reich. Using all three of these gifts as an historian, Irving wrote several books about Hitler, the Third Reich, and the Second World War, largely drawing on primary sources, and arrived first at the conclusion that Hitler hadn't had any knowledge of the Holocaust, and later at the conclusion that Hitler hadn't known about the Holocaust because there hadn't been any Holocaust. He preached Holocaust denial passionately and prolifically and had a habit of suing people for describing him as a Holocaust denier (a habit which eventually bankrupted him).
Did Irving tell a true story? Most certainly not. But did he do history? That's difficult to deny. He researched the past, used the facts he discovered to form an opinion, and argued that interpretation of the past with supporting evidence. If that's not doing history, I don't know what is. But he also misrepresented facts, misinterpreted facts, reached and rather tragically squandered the gifts of a very capable historian dedicating his work to trying to keep himself in the right in the face of a mounting body of evidence that showed that, in fact, he was categorically wrong. The heart of the issue is that in order for history to be "true stories" we would have to know in a perfect, objective sense exactly what happened and why. We don't, and we never will. Instead, history is our best guess, what we think happened, and why it happened, and what that meant. The past is what happened. History is how we talk about it.
For sources and further reading
On Irving's work and views: Hitler's War, The Trail of the Fox, and The Bombing of Dresden - David Irving
On Irving's reception by other historians and his work on trial: The Holocaust on Trial - D. D. Guttenplan, Lying About Hitler, Richard Evans
On the philosophy of history in general: What Is History? - E. H. Carr, History: A Very Short Introduction - John H. Arnold,
History as an academic pursuit is more of a way of understanding and interpreting the past as the1Man has pointed out. He mentioned Carr, so I believe this passage from is book is a good one to highlight. Carr defined history as,
"a continuous process of interaction between the historian and his facts, an unending dialogue between the present and the past."
It's a solid definition. Historians are often tasked with gathering available evidence to try and figure out not only what occurred in the past, but how it relates to the present. This generally results in the controversies of history, because being dispassionate and fair are often difficult things to accomplish in historical writing. We begin our research projects with our own biases intact and often fail to fight against them. We sometimes interpret the facts as we want to interpret them.
Therefore even Carr's definition can be somewhat philosophically debatable. I have always skewed more to the side that historians should first focus on where the research leads them, free of preconceived notions (and if not, maintaining an open mind). Then the event should be placed in the perspective of when it occurred and what it meant to the people who lived through it. Then lastly, using what we have researched to make a statement about how it is relevant to the present. This is a little different than Carr's "unending dialogue," but I think it reasserts the notion that history is history, and not always present day social commentary.
But of course, these are not hard and fast rules. Historians are always at liberty to approach their work in the manner they see fit.