My impression has always been that “nonplussed” means >
It means the same thing as nonplussed, addled, befuddled, disconcerted, discombobulated and confounded do - confused.
I learned both nonplussed and bemused so young I never had the opportunity to assume they meant something else.
That’s what I think, too - different words with slightly different meanings allows for a wide range of nuances.
The problem with this is that the connotation you give to bemused occurs (AFAIK) only due to the similarity in sound. The actual connotation I infer from the entry here is one of puzzlement. To bemuse someone is to cause them to have to think about something, i.e., to muse it over so as to understand it.
I think I’ve always thought of it as something in between. It’s a very deadpan sort of confusion.
I didn’t truly take notice of the word nonplussed, until I heard someone use it about 10 years ago. Then it seemed like everyone was using the word. Perhaps confirmation bias. Anyway, I looked it up having no idea what it meant, and found that most were using it incorrectly.
I tried tossing the word in conversation or email at first, because the word is compelling for some reason. I want to use it. But now I refrain from doing so, since if misinterpreted, it’ll change the meaning to the exact opposite of my intention.
So now I just substitute it, depending on context, with something everyone knows like, speechless, gobsmacked, mortified, surprised, shocked stupid, etc…
I find it interesting that all three usage examples on the Google dictionary page for nonplussed use the word to mean unperturbed.
I would imagine that the majority of people use it this way. If that makes me a descriptivist, then so be it, but I think the “surprised and confused” camp are fighting a losing battle.
Personally, I don’t use the word at all because of the potential for misunderstanding.
The answer is #2. My dictionary also says that in recent years the word has also been used in the #1 meaning, because people think that the ‘non’ is the negative prefix.
Edit: I usually see this word used in older books.
Confused
I sometimes wonder when I’m writing correctly, how many people think I’m making mistakes because they don’t know any better. {Shudders}
It means confused, and I only know that because of a great Cracked article about commonly misused words.
These kinds of words are my favorite, because I get to have someone try to tell me I used it wrong, looking their noses down on me and then, Surprise! I used it correctly!
ETA: Exactly Cat Whisperer. In writing, they would think you were ignorant, because you aren’t there to correct them. But in real life, it can be fun to watch them try to ‘correct’ you.
As a descriptivist, I accept that words shift in meaning and that that is a fine thing. There is no moral necessity for words to retain their original meaning or form. No one today objects to cherry or pea, and no one cares that aks is an older form than ask. Eventually, the day will come when no one will object to using nonplussed to mean unperturbed, and that is fine and appropriate.
As a descriptivist, I can tell you that that day won’t come until I’m dead. 
Here is the Cracked article. Love those words. Always trying to remember to wedge them into conversations.
Descriptivist stormtrooper here, albeit one who sees a use for having a “standard” form of the language that educated people use in writing (and I generally prefer to do so myself). But I don’t see how with a word like this, it can make any sense to say that “most people use it incorrectly”.
I say “a word like this”, because there are certainly many examples of words that are used in a nonstandard way by less educated people, while still used clearly and effectively in the standard way by the better educated. But this word, it seems to me, is not even used at all by working class types–is it? Therefore it is, as described in the comments above, a kind of troublesome word at this point because it is understood to mean different things by educated people who otherwise generally communicate in the same lingo. And not just different things, but nearly opposite usages that can be ambiguous in context (which is, really, the only way I expect something like this could happen to begin with).
So I do think the word is basically ruined. If everyone were “using it wrong”, then we’d be fine: it would just have a new meaning, and it would be a historical curiosity that its meaning had reversed (like the way the maps of presidential elections look so similar to the way they did in the late 19th century, except with the parties swapped). But right now, it just has way too much potential for confusion (not to mention that irritating possibility of having people think you’re “using it wrong” no matter which way you use it).
What I’m really curious about is how this came to pass. Lots of words drift into having different meanings, or multiple meanings. But how can a word drift from meaning, approximately, “fazed” to “unfazed”? I wonder if BigT’s comment provides a clue:
I remember thinking “unhappy” was fairly close to its meaning when I first encountered it in the 1980s. Even closer to my sense of it would be “cross” or “mildly irritated”. As in, “Joe arrived at his car and was nonplussed at finding a parking ticket on his windshield.”
So can it navigate from there to “unfazed”? Or is it more likely that this shift came (at least at the beginning, before any critical mass built up on the nonstandard usage side) from people reading ambiguous phrases and misinterpreting them? For example: “Jane was nonplussed at learning her mother had decided to move to Florida.”