Someone claimed I'm making the No True Scotsman Fallacy, but I believe they misunderstand it, and their logic is flawed.

I was having a debate with someone who claimed I made the No True Scotsman Fallacy, because I said they were wrong about the definition of something. However, I am very certain I didn't and believe they are making a fallacy instead, but I do not know what the name is, or if it really is one. It's a sensitive topic, so to be slightly less offensive I'll describe it as so: essentially, I was making the argument that sex an rape are mutually exclusive, sex can't be rape, and rape can't be sex, because once consent is broken, it becomes rape and no longer sex. The other person was essentially arguing that I made the NTS fallacy, and that (in more sensitive terms remember) sex is rape. However I argued that what they learned to be sex, was actually called rape, and one can have sex without it being rape. That's is when they claimed I made the fallacy. I know it's a little confusing, as I wanted to keep this "PG" or "PG-13," but my question is, is it a fallacy when you use the wrong definition for something, and is is even a NTS fallacy when you haven't narrowed the parameters? Did I perhaps make a different fallacy? I believe the topic of debate is mutually exclusive, while the other person believes they are not, but by definition, it has to be mutually exclusive...

I am curious as to what definition of sex and rape you are using. "Rape" is defined as "unlawful sexual activity..." which, by necessity, includes sex. Sex does not require consent... "consensual sex" requires consent. Words like "unlawful" and "consensual" are applied to "sex" because sex simply refers to the physical act(s). I don't think the No True Scotsman fallacy applies here, but it does sound like you might be guilty of the Definist fallacy, which is changing the definition of terms or using very rarely used definitions in order to support a claim.

Firstly it's important in discussions to agree on a definition of a word, otherwise you can have people making cases based on entirely different things. Sex is fairly vague and, while I understand what you most likely mean by it, your definition is only one of a range of definitions. Bill Clinton famously had a different idea of what sexual relations meant than probably most people.

So, whilst you consider sex to be a consensual act, rape is technicality a sexual act, whether it's sexually motivated (though it may not be), or a sex crime, or simple considered a sex act by the mechanics. There are other terms which are less ambiguous, and I suspect in trying to be polite you may have substituted one as it's swearing or profanity, but which I would consider to be a consensual act, but again you're better off discussing and exploring the definition and trying to come to a concensus rather than just have your own intransigent opinion and be damned.

On the topic of no true Scotsman, which irrelevantly I am, my initial reaction is absolutely not.* That requires a category or classification of person, with a claim that they don't do something. Two classic examples of this which I grew up with are that no true Scotsman :

• has underwear beneath their kilt
  puts sugar on their porridge
  

Both are factually incorrect, tradition does not disqualify someone from a nationality. In fact it's a form of bigotry, dismissing someone else's opinion simply because it doesn't match your own.

Obviously this doesn't just apply to Scotsmen, so an example may be no true Liverpool supporter would want Manchester United to win in the champions league.

*Without seeing exactly what was said I can't say for sure, but I can't imagine how what you described could be NTS. Is there a different fallacy? Possibly argument by pigheadedness<>?