It's both. It's a mistake to define these things solely in terms of whether they pretend to be in the same universe/continuity or not. Continuity is just a storytelling device, not the end-all and be-all of fiction. The real purpose of a "reboot" or reinvention is to tell a familiar story in a new way that revitalizes it and brings in a new audience. Starting a new continuity like Galactica or the Marvel Ultimate Universe did is one way of doing that, but so is continuing what's supposedly the old continuity but in a fresh way. Continuity is just a tool in the kit; the real goal in either case is to take something old and make it new and different while retaining its core essence.
And really, the new Who may follow the conceit of being a continuation, but in actual fact it's a reinvention in a lot of ways, a major reinterpretation of how the universe works and what its history is. Which, of course, is something the original Who did many times before, and that the 1996 TV movie did as well. The difference being that the new series has made it explicit that a massive temporal upheaval, the Time War, was responsible for all the changes in history and continuity between the old series and new -- which, as I already said, is essentially the same thing that the Abrams Trek movie did. The difference is only in detail and degree.
And seriously, if you pay attention to fiction at all, it's easy to find many examples of continuations that were supposedly in the same reality but in fact rewrote the continuity drastically. The Marvel comics published today, set in 2012, pretend to be a continuation of the same universe where Reed Richards launched his rocket to beat the Soviets into space and Tony Stark was wounded in Vietnam, but of course they've rewritten all the period details of the continuity over and over again. The pretense is that it's a continuous, consistent universe, but it obviously isn't. Then there's something like M*A*S*H, an 11-year series about a 3-year war, whose date references got up as far as 1953 before getting pushed back to 1951 in later seasons, yet which still had the characters' relationships and history informed by events from that earlier, contradictory chronology. Or I Dream of Jeannie, which spent the first two seasons insisting that Jeannie had been born human and cursed to become a genie, but then rewrote history so that Jeannie had been a genie by birth and had genie parents and siblings. Or War of the Worlds: The Series, where the first season was set in a fairly normal present-day world but the second was suddenly a decaying, post-apocalyptic near-future dystopia without any explanation and without any significant passage of time (since the preadolescent member of the cast had only aged a few months in the interim).
So it's naive to say there's a fundamental difference between being in the same universe and rewriting the continuity. A lot of shows pretend to be in a continuous universe and rewrite the continuity anyway. Which is why you can't take continuity too literally or seriously in these discussions. It's ultimately all just pretend in any case, and that means the creators can pretend it's consistent even when it purposefully isn't.
