The Doctor is Out

[henry quirk]

glatt,

It's been central to the series, for most of the series, that the Doc, as a Time Lord, can regenerate, that is, become essentially a new person.

Sometimes this happens by choice; sometimes by accident.

With the Doc: regeneration is almost always because he puts his dumb ass into untenable and lethal situations.

So: when the Ninth is referred to, yeah, you're talkin' about the ninth regeneration of the Doctor, the ninth 'new person' to take up the name 'Doctor', sharing with the other incarnations mainly memories, but little else. That is, each is a distinct individual, not merely a continuation of the previous version.