Yeah technically it is in the same universe. And no he won’t be the same character, he’ll just be the Doctor. For the first 4 seasons of Doctor Who (of the 2005 reboot) the head writer of the show was a guy named Russell T. Davies…he also is responsible for Torchwood. When the 10th Doctor/David Tennant left the show he did as well. The new head writer since season 5 and onward has been Steven Moffat (also responsible for Sherlock). So there are some inconsistencies (and Moffat is kind of a bag of dicks so he tends to ignore Davies era/his characters/and Torchwood like the plague). BUT it’s still a great show. And I’m not sure if you know this but the Doctor is a species of alien called a Time Lord (when they are seriously injured and about to die so long as the death isn’t instant they can ‘regenerate’ – every cell in his body changes and he essentially gets a new body; hence the multiple actors playing the doctor). Yeah so he can probably live forever.
I feel like I got sidetracked somewhere in there heh