I would argue that the first is annoying because we associate names with specific ingredients and flavors. If you mix up a Manhattan and call it a Daquiri your lying. There's a precedent of this kind of thing happening out in the wild so it does get annoying. "Martinis" are the biggest offender.

And any stemmed glassware is designed that way so you don't need ice in the top, since you shouldn't really be touching the part of the glass that actually holds the liquid. Also drinking it that way sounds horribly awkward.

I would agree it's shitty to actually be mean to someone who makes mistakes like that, but there are at least reasons for pointing it out.