It’s all a matter of personal taste/judgement, I feel.
Some people will refer to those Tennant specials as the 2009 specials, even though one episode airs in the following year. Some will refer to it as Series 4, for some reason. And some will combine both and call them part of the Series 4 Specials.
It’s far easier to just go with Specials, IMO.
I still find it baffling I went nearly 20 years with this special interest and only found out here people don’t agree on which Christmas ep belongs to which series 
I don’t envy you lol.
According to IMDB, Series 11 has a Christmas Special - Twice Upon a Time should have been included in the Whittaker boxset. Madness.
Baffles me truly. How is Voyage of the Damned series 4? Anyways back to images!
But then they did steelbooks for the Jodie specials
We only have to agree to live.
Sadly, we can only agree to die.
I genuinely thought that specials were just normal episodes of the series that preceded them when I first watched doctor who, because I caught up with it all on iplayer and didn’t see the dates that they aired. So while it’s true that specials are not part of any series, it also feels like if they were, they would all be part of the one that precedes them. In my mind, all the specials from Eve of the Daleks to Church on Ruby Road are part of a 13-episode-long series 13.
I’m biting I can’t resist the reason its on the s2 dvd is because from a viewpoint of wanting to sell the most dvds, why would they wait MONTHS to do a boxset of s1 with the christmas ep, when they could do a boxset immediately after the series airs, then do a single release for the Christmas ep.
Yup. Same with the official website, which splits them off from any series, such as here (search by Tenth Doctor, for example, and scroll):
I know. I’m just saying that the BBC have put out The Christmas Invasion under the marketing title of Series 2 with that DVD. But then they’ve also put it under Series 1 on iPlayer. On their official website, it’s not part of either. So my general point is even the BBC is inconsistent, and it’d be silly to go off just one when there are various contradictions.
(Also, in fairness, they could’ve put out The Christmas Invasion in that ‘Volume’ style on its own with its Confidential, but hey, they didn’t :p)
Doctor Who episode listing is a nightmare - iPlayer have one order, home media another.
The Christmas Invasion is quantum-locked.
It’s in a season of its own, unless you look at it on iPlayer than it’s part of Series 1, or if you look at it on DVD it’s part of Series 2.
Just don’t blink!
I don’t trust iPlayer. They start Season 1 with The Dead Planet 
/j
They also say the show started with the daleks!
That’s because if he-who-must-not-be-named.
There isn’t even a Series 13. It goes Series 11, Series 12, Flux…
Silly iPlayer.
