Ahhh, there is the word I was looking for. "Characterization".
I have to admit, I tend to think that role playing and characterization go hand in hand. But, CJ, you do make a darn good argument.
Let me try to take a slightly different stab at the beast. If I watch someone play their character for a session or two, I should be able to pick up that character sheet and there should be no surprises, IMO. If the player is playing a highly intelligent, tactical character, then I should see a decent Int score on that character.
OTOH, if the player is playing very tactically, turning his characters into some sort of Special Forces operative who never makes a mistake, and I pick up the character sheet and its got an 8 Int and 6 Wis, there's a disconnect.
For my own sense of immersion, there should never be that disconnect. Note that should is the operative word there. We all overplay our characters from time to time. If you're reading this, you've probably been gaming for a number of years and you don't make the rookie mistakes (most likely) anymore. Yes, your character is carrying those silver weapons "just in case". Yes, you search for secret doors. Yes, you listen at doors and don't just open them. That sort of thing.
We all do it. And, by and large, so long as it doesn't get too out of hand, it's not a big deal.
But, as I said, if I pick up a character sheet and go, "huh? What?" then someone, somewhere along the line has failed to characterize that character very well.
Or, to put it another way, if you're playing B.A. Barracus, don't be Face. For me, it's very immersion breaking to know that you are playing a character other than what's in front of you. In my mind, the measure of a good roleplayer is how well he can portray the character he created.
Characterization, to me, is probably the most important element of roleplay.