When is a companion not a companion?

If you have read the Radio Times Companions Special (still available) you will have noted that there is a total of 48 companions listed - from Susan through to Rory. Happy with that? I'm not. I say the figure is actually 36.
The discrepancy arises for me due to the question - how do you define a Doctor Who companion? There is a lot of debate about this. Some people say the person has to have appeared in more than one story. Not enough on its own - as we never count Alpha Centauri or Aggedor, do we. Not just more than one story, but consecutive stories then. Still not quite enough. Usually, travelling in the TARDIS has to be added. By this reckoning, poor Liz Shaw doesn't make companion status even though she clearly is one. I'll make the special case for her shortly. But first, lets get Romana out of the way.

The RT Special counts both Romana I and II as separate companions. This is clearly just to acknowledge the two actors individually - Mary Tamm and Lalla Ward. The fact is, it's the same companion. It's two incarnations of the same person. We talk of eleven Doctors - but what we are really meaning is eleven incarnations of the same Doctor. Whilst claiming two Romana's, the RT Special only has one K9 - when there are clearly two. K9 Mark II might have some of the same programming as its predecessor, but it's an entirely different physical entity. There are two K9s. (Before you ask about Mark III - see below).

Is the Brigadier a companion? I'm going to be slightly controversial and argue not. The reason for my decision forms the crux of the matter. I contend that there are 3 categories of people who often get lumped together as "companions". These are:
1. Full companions.
2. Recurring / returning characters.
3. A character who fulfils the companion role for the duration of a particular adventure.

Characters which the Special lists as companions, who I believe belong in category 2, include the UNIT triumvirate of the Brigadier, Sergeant Benton and Captain Mike Yates. Also fitting into this category would be Jackie Tyler and River Song. K9 Mark III doesn't get a separate mention in the Special, but it also fits this criterion. Mickey Smith starts off as a recurring character, but as of School Reunion he gains full companion status.
I'm putting Wilf Mott into this category as well. He starts off as a recurring character, but then goes on to become a category 3 character - fulfilling the companion role in The End of Time 1 & 2.
You might feel tempted to put Kamelion into this category. He appears in more than one story but certainly not consecutively. It's clear though that, just because we don't see him on screen, he's there in the TARDIS all the time from The King's Demons through to Planet of Fire. He's a full companion.

The category 3 characters begin with Sara Kingdom. She takes on the female companion role after Katarina's demise - but the character appears only in this one, albeit massive, story. Viewers at the time would certainly have taken her to be the new companion - but in hindsight they got it wrong.
The other category 3 characters are Grace Holloway, Astrid Peth, and the various characters who appear in David Tennant's final "specials" series - Jackson Lake, Lady Christina, Adelaide Brooke and, as mentioned above, Wilf Mott. They're all classed simply as companions in the RT Special, but I'd argue they're not.
There are many characters throughout the history of Doctor Who who play a significant role, and even get a trip in the TARDIS (Sir Robert Muir, Lawrence Scarman, HG Wells etc, etc), but we don't call them companions - so why these ones? As I said, they are playing a surrogate companion role - and only that.

And what of Liz Shaw - who might fail some people's TARDIS test? In the early 70's, the word "assistant" becomes interchangeable with "companion". That's because the Doctor is stranded on Earth, working for UNIT, with a TARDIS that doesn't work. Jo Grant starts off as the Doctor's assistant - not companion - taking over from Liz. We accept Jo as the "companion" character right from Terror of the Autons. Had the TARDIS been working, Liz would definitely have gone off with the Doctor on his travels.
Regarding category 1 - the full companions - longevity isn't an issue for me. Doesn't matter whether you get two stories or twenty two. Katarina and Adam Mitchell are just as valid as Susan, Jamie, Sarah, Tegan or Amy.
So, I make Oswin, or whatever she will actually be called, the 37th Doctor Who companion - not the 49th...