Regardless of the distinction, The Doctor’s essence was within in each and every Gallifreyan, which angered The Master beyond comprehension, and it was that knowledge that caused him to burn the world to ashes, all the while resenting The Doctor for technically being the source of his own power.
Oh yeah, and this means that Jodie Whittaker’s Doctor is a completely different species than the “Time Lords,” or possibly the only true Time Lord.
The revelation not only explained how Doctor Who’s broke the twelve-regeneration rule, but it also made the Time Lords a hybrid species that was only advanced by The Doctor’s foreign DNA.