From the point of view of
the structure of a player's engagement with the game, there is no difference between the following two states of affairs:
*Your character is unconscious, so you can't declare actions for them until they recover.
*Your character is petrified with fear, so you can't declare actions for them until they recover.
Both states of affairs have the same structure: the player is precluded from declaring actions for their PC. The difference of fictional colour (unconscious vs frightened) doesn't affect that basic structure.
Similarly, from the point of view of
the structure of a player's engagement with the game, there is no difference between the following two states of affairs:
*GM to a player whose character is proceeding northward: There's a wall [lake, forest, river of lava, whatever barrier you like] in front of you, so you can't keep moving northward.
*GM to a player whose character whose character is advancing through a company of soldiers by cutting down everyone who gets in their way: You see the person you love right in front of you. Your advance halts, as you can't cut them down.
Both states of affairs have the same structure: the player's desired action - move northward/advance through the enemy - is thwarted, for a fictional reason narrated by the GM: in the first instance, that fictional reason is a barrier to movement that the character can't overcome; in the second reason that fictional reason is a person the PC won't cut down.
Now, many RPGs have rules that mean that obstacles the GM presents are prima facie, rather than absolute: that is, when the GM narrates an obstacle in the fiction, the player is entitled to declare an action to overcome that obstacle.
With this in mind, maybe in the barrier example, play proceeds like this:
*Player: A wall/lava/lake/forest isn't going to slow me down - I proceed through it!
*GM: OK, make a roll on Indomitability [or whatever skill/ability/attribute/etc is applicable, given the game's PC build and action resolution rules].
And maybe in the love example, play proceeds like this:
*Player: I'm not going to yield to sentiment - I harden my heart and cut them down!
*GM: OK, make a roll on Brutality [or whatever skill/ability/attribute/etc is applicable, given the game's PC build and action resolution rules].
Again, the basic structure is the same although the fiction is different.
Some RPGs are very clear on how fiction is established, who gets to establish what fiction, who gets to change the established fiction (and how), etc. Some are not.
And some RPGs are clear on how fiction translates into resolution; some are not.
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These issues of
clarity is separate from the issue of
does this produce good/compelling play? For instance, in AD&D the rules draw a clear distinction between
the GM's narration of living dead in the form of skeletons or zombies - where the player is free to decide the fiction of how their PC reacts - and
the GM"s narration of living dead in the form of mummies or liches - where the game calls for a saving throw to avoid the PC being struck by fear.
In AD&D the rules are also clear about how fiction translates into resolution: a player who describes their PC's teeth chattering at the sight of a skeleton, is nevertheless entitled to declare, a minute later, that their PC wades into melee with those skeletons unperturbed by the horror and un-penalised by their chattering teeth. The narration of fear is mere colour, that doesn't affect resolution.
Likewise the rules (in the AD&D MM) are clear that numbers grant a bonus to the saving throw vs a mummy's fear, but not v a lich's. In the latter case, a player might describe their PC as drawing comfort from the presence of their friends, but that is again mere colour.
Personally, while I find all this clear enough, I don't think it produces especially good RPGing. Why does the sight of a mummy - the walking dead - potentially petrify with fear, but not the sight of a skeleton, although the latter is also walking dead? Why do numbers boost confidence against mummies but not liches? Why does a player who narrates their PC's teeth chattering, not have to then suck up a corresponding penalty when melee breaks out? Or to put it another way, a player who narrates their frightened PC suddenly bucking up when the fight breaks out is not producing especially compelling fiction.
That's before we get to possibilities like a company's leader - say Aragorn, or Tanis, or the like - trying to break the hold of fear over a petrified companion. This is a common enough thing in fantasy stories, but not something that the AD&D rules provide for when a group of PCs encounters a mummy.
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In many RPGs - including AD&D - the fact that a PC loves someone is generally irrelevant to action resolution. The only constraint on a player narrating their PC's love for a person one minute, and then cutting them down as part of the inexorable advance the next minute, is good taste.
The Charm Person or Suggestion spells are an exception to this, because they use notions like "any word or action . . . will be viewed in its most favorable way" (PHB p 55) and "must be worded in such a manner as to make the action sound reasonable" (PHB p 75). Suppose that a player, whose PC is under the affect of one of these spells, points to some fact of friendship between their PC and another character in the context of explaining how and why their PC reacts to a particular request. (Eg "I wouldn't just cut down Gutboy when requested to do so, because Gutboy is my friend.")
Now suppose that, some time later, the PC is cutting their way through a horde, only to see that same character - their friend - standing their in front of them, one of the enemy soldiers. Is the player now just permitted to say "My PC doesn't care anymore - I cut them down!" This is what the AD&D rules seem to imply: a PC's emotions can be as fickle as the player wants, switching on or off at will. But that doesn't seem conducive to especially compelling fiction.
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I haven't said anything about the 5e D&D Intimidate and Insight skills. To me, the 5e D&D rules on what skills are for, and how they relate to the fiction - both fictional positioning, like
Am I free to just declare that I cut down my friend without consequences? and fictional consequences, like
Am I just free to declare that my PC is unpersuaded by the charlatan, although the charlatan has hoodwinked everyone else they've ever dealt with? - seem pretty unclear.
It seems that, when the game designers want the fiction to have any sort of teeth, they bypass the skill rules and use other build and resolution elements, like a dragon's Frightful Presence or a mummy's Dreadful Glare.