Yeah, yeah. Thats why reddit has r/animatedgifs and not r/gifs for posting animations. OH WAIT!
But it doesn't matter. The word belongs to YOU and who dares do with it what people do with every word? OWN it and change its meaning over time.

So if someone says "I saw a ridiculous gif today", she is an idiot. Because she doesn't know 'the difference'.

No.
I'm sorry.

No, they don't. But they get used in not technical environments, and their meaning just changes. That's a fact on language and live.
Someone who sends me to fuck myself is an asshole, no mother what you fucking bully say. And so are you.

Words mean... whatever people decide they mean. Unless you are on a technical enviroment. Or an asshole environment. If someone on the street talks about a gif he saw, and you later find out it was really a PNG, please, please, shut up.

Nowadays gif means 'short animation', much more than a particular format. Slashdot seems to be full of cranky Statlers and Waldorfs this days.