I’ve heard the French occasionally use si instead of oui for yes. Is there some subtle difference in the usage or do both terms convey exactly the same shade of meaning?
“Si” is in response to a negative question to contradict it in the affirmative.
So, like where in English you might have an ambiguous construction like “Do you not like carrots?” “Si!” would be “Yes, I do like carrots” as opposed to “Yes, I do not like carrots.”
The only time I ever answered “si” in France was when I momentarily thought I was in Spain.
Exactly right. “Si” is an emphatic yes in response to a negative statement or a negative question
If a Frenchman asks me simply, “Es-tu American” (Are you American?), I would answer, “Oui, he suits Americain.”
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But suppose the Frenchman thought I spoke French superbly, too well to be a Yank. He’d ask, “Tu n’es pas American (You’re not American, are you?)” And I’d answer, “Si.”
If you said “Oui, he suits Americain”, no one would think you spoke French superbly. 
That was a joke in the first place (I speak both French and English with a Queens accent).
But spell check turned my written French into something unrecognizable!
Interesting that it kept “Americain” the second time. (Though not the first time, oddly.)
I thought it meant an American in the Paris fashion industry…
I always learned that “si” in French meant “if”.
So is “si” sort of like the slang US quasi-negative answer “as if!”?
“Si” more commonly means “if.” But using it to mean “yes” means you are contradicting a negative statement instead of agreeing to it. It’s like this in English:
“You’re not going to work?” “Yes.”
Now in English, the “yes” can mean “Yes, I’m not going to work” or “Yes, I am going to work.” More words are needed to clarify.
In French, using “Oui” means “Yes, I’m not going to work,” but using “Si” means “Yes, I am going to work.”
No, it is not slang. It’s standard French grammar that they teach you (or at least they taught me) in high school French when answering a question posed in the negative affirmatively in contradiction.
I also learned it as basically a synonym of “tellement” (meaning “so”).
Article on uses of si.
They have separate etymologies. Sī (=“if”) is from Latin si (“if”); si (= “yes” in response to a negative question or “so”) is from Latin sīc (“so” or “thus”). The two Latin words are definitely separate words but probably related.
French has two words for ‘yes’, one for agreeing with an affirmative, the other for disagreeing with a negative.
English once may have had the same distinction, with ‘yea’ corresponding to French ‘oui’ and ‘yes’ (a contraction of ‘yea so’) corresponding to French ‘si.’ (*I learned this at SDMB. *
)
Shakespeare used ‘Yes’ almost exclusively in this contradictive form; note the distinction between ‘Ay’ (a synonym of ‘Yea’) and ‘Yes’ in this passage:
[QUOTE=All’s Well That Ends Well]
PAROLLES. My lord, you give me most egregious indignity.
LAFEU. Ay, with all my heart; and thou art worthy of it.
PAROLLES. I have not, my lord, deserv’d it.
LAFEU. Yes, good faith, ev’ry dram of it; and I will not bate thee a scruple.
[/QUOTE]
While English uses ‘No’ to make the normal agreement with a negative query; Thais may use the Thai equivalent of ‘Yes.’ And Thais speaking English may say ‘Yes’ in those contexts where native English speakers would say ‘No.’ Hilarity ensues.
English definitely did have that distinction, the words were “yea” and “yes”. I forget which one was which, but there’s a letter from Thomas More where he was pedantically explaining the distinction by correcting someone else’s writing. Amusingly More apparently got the two words wrong, which suggests that even in his time people were ceasing to remember / observe the distinction.
Maybe (it’s about equally likely the “-s” is from the old subjunctive of “be”).
No, those are two different "si"s. One is for “if”, the other is for “your negative sentence is not correct” - while they are homonyms they’re not the same word at all. Even their etymology is separate.
A couple other examples:
In Arabic, نعم na‘am is the positive yes and بلى balá refutes the negative.
In Persian, بله baleh is the positive yes and چرا cherā refutes the negative.
Navajo language does that too.
Their Spanish sisters are one of the word pairs where the accent mark serves exclusively to differentiate two monosyllabic words: sí, yes (both to agree with a positive and to refute a negative); si, if.
My understanding is that si as yes was only used in some parts of France. I’ve never seen it in Quebec French nor been taught that. I do recall many Pink Panther episodes where Clouseau admonished “Don’t say si, say oui.”