I think most of the confusion of the users come from how and where they learn about the characters.
Let's say that most of users know about Miku, Teto, or any other popular character, from Project Diva (there is Teto's extra DLC), from official concerts, or from popular songs available online.
If a user knows from Project Diva or Project Sekai, probably will think that Sega is actually behind all of those characters. Which, to be honest, is someway true: Sega holds all the rights of Miku games on all platforms, developed by Sega and other companies. Sega also is responsible for making the concerts, with its company Marza Animation Planet. And Sega designed many of the original modules for both Diva and Sekai (others were based on official illustrations/song or Piapro art contest).
Now, I feel there are two kinds of user: user n.1 likes those songs and characters, but not so much by investigating more about them. They are Vocaloids made by Sega. Yes, that's it. But for user n.2 things are different: will research more about them, on official websites, wiki, and so on, and will understand the various differences, the different engines made by different companies, why Crypton has both Vocaloid and NT, why Teto, IA and Gumi have different outfits for different engines. And will learn about new characters. So it's ok and a good thing to correct new fans, especially if it's user n.2 type.
Vsynth sounds very good (and technical), vocaloid of course is more iconic. With so many different engines available now, I usually just say [character]+[engine], is just easier for me. For example, Miku V6 or Miku NT2, or if I want to compare some of her previous VB (voicebanks), I say Miku NT (which can still be used, if you have the installer), Miku SP (Super Pack), Miku V3, Append, ..
I think Yamaha, Crypton and the other companies should translate some of the books that are available in Japan and that can explain very well the history of voice banks.
