They are never the same thing.
I disagree. Vigorously, even.
... but acting out dialogue and such is neither necessary nor sufficient for playing in a way that's true to your character.
How do you determine what's "true to the character"? And
who gets to determine that? (if not the player, through the act of actually playing the character, which can include speaking for them and coming up with their ideas).
The character doesn't
exist until the player defines them. Sure,
part of the definition is the mechanical stuff, but the rest of it, and to my mind the vastly more interesting part, is the definition that comes from real play, from the player making decisions
and saying stuff.
Surely your character shouldn't deviate wildly from what's written there.
So you've never encountered a PC with the intellect of Einstein who did stupid things?
Or the a PC with the wisdom of Solomon who did unwise things (more on par with Solomon Grundy)?
Or a PC with the charisma of the young, slender Elvis who did things with all the
savoir-faire of the pill-addled, fat, old, Elvis, slurring words out of a mouth stuffed with half-chewed deep-fried peanut butter sandwich?
Surely, if we were in the mood to give an honest account, when it comes to the mental stats, most players have no choice but to
deviate wildly from what's written on their character sheets, because said players simply aren't among the smartest, wisest, and most charming individuals in the world.
Like their characters often are.
Which is why I accept a PC's stats invariably tell only part of the story. The other part is what the player brings to the table: their skills, natural abilities, and experiences, which sometimes exceed those of their characters, but most of the time, fall far short.
Yes, the character is more than what's written on the sheet, but surely it has something to do with what's written on the sheet.
Yes. Of course.
An example: I'm currently running AD&D. The PC's CHA scores affect their max. number of henchmen, loyalty base, and reaction adjustment (which I prior to any negotiation w/NPC's). That's all the system cares about, and that's fine by me.
But their CHA says nothing nothing about the qualities of their lies, the actual meat of their negotiations --which are less about charm and more about smarts/tactics, anyway-- and has no bearing on how they choose to characterize their PC's.
Even 3e/Pathfinder, with their more detailed social skills, don't really say a whole lot about how effective a character is in social situations, if you look closely at the skill descriptions. Bluff is good for short term lies ("these aren't the droids you're looking for") and Diplomacy affects overall attitudes (like AD&D's reaction rolls). There is plenty of room here for lower CHA characters to be effective in negotiations and longer-term acts of persuasion.
Would you (in a pre-4E context) allow a character with a 9 strength to (in the normal course of events, not as part of some unusual maneuver) claim a +3 strength bonus to his melee attacks and damage?
No.
However, if the
player of the STR: 9 character decided to use a
lever to help move a heavy object, I'd definitely grant them a bonus, if not let them succeed outright.
Which neatly illustrates my point. Character stats define raw ability, which can be modified by clever ideas from the player.
...why should the player with the 9 charisma character get to be as, if not more, charming and persuasive as one with a 16?
Because the player with the CHA: 9 chose better words to say.
Let's change the example a bit (I like doing this

). Player A is running a 7th level wizard with an 18 INT. Player B is running a 4th level wizard, A's less experienced former apprentice, with an INT of 15. Both have memorized comparable, effective spells.
I think we can agree, effectiveness-wise, Player A should be > Player B.
But during an encounter, Player B saves the the day by using their spells more effectively. Even though, on paper, Player A has the stronger PC.
Does Player A have the right to complain that they were overshadowed by Player B? Did Player B play poorly by playing smarter than Player A?
Mechanical (character) ability can only matter so much, if this is going to be a game where player contributions matter. Now we can debate exactly how much influence player ideas/words should have, and in what situations, but to deny their place, or label it bad role-playing, is, well... silly.
I define it as making decisions chiefly because they're the ones your character would make in that situation, as opposed to the many other reasons you might base them on.
How does a player determine an action is one their character (and not them) would make? Without actually making it. Therefore, making it, when push comes to shove, their decision. Something of a paradox, eh?
My question to you is, can someone not be doing that and still be role-playing, by any reasonable definition?
Yes.
Any decisions my characters make are the ones I choose. By definition. My
reasons for each of them may vary. But all of them are 'true to the character', because I'm the guy who determines
who the character
is, and thus all of them constitute role-playing.
Your definition of role-playing is rooted in a denial of the inherent overlap between player and character. I can pretend I'm only making the choices my character would --and I often do!-- but its just that, a mini-game of pretend inside a larger game of pretend, which hardly provides a solid foundation for a definition of role-playing.