This and the 1963 series are the same show, with season 26 ending in 1989 and season 27 starting in 2005. The BBC and all other companies involved, classified the show, when is started up again in 2005, as a new, separate show, calling the 27th season, season 1. This was done to avoid confusion for new viewers. They mainly achieved the opposite, because, by classifying the 2005 pickup as a new show, they confused the large fan base that was already familiar with the old series. Many questions were raised with this "new show", some of them include:
Is this a reboot?
Is this a different Doctor?
Is this an alternate timeline?
When does this take place?
Is this a different actor playing the same Doctor?
The answer to most of those questions are: no. This series is completely canon, and a direct continuation with some time having passed between the 26th and 27th seasons. To avoid as little confusion as possible, without having a bunch of stuff explained to you from outside sources, this is how the shows and movie should be interpreted; There are seasons 1-26, following the first 7 Doctors' adventures, then, what one could call, season 26 1/2, which would be made up of the 1996 tv movie "Doctor Who", the mini episode "The Night of the Doctor", and an edited version of the episode "The Day of the Doctor". With "Day of the Doctor", having some of the scenes with exclusively Matt Smith and David Tennant chopped down or removed. A tiny bit confusing, but then we continue with season 27-33 and onward. Even if TV stations count the new seasons as different shows, websites like wikipedia and imdb need have them as the same show, it'd be a lot less confusing and a lot more convenient. Lots of shows have stopped for a while and continued later, one example is Futurama, that show ran from 1999 to 2003, then from 2008 to 2013. that was classified as one continuous show, and so should doctor who.