Why do so many people misunderstand Yandere?
Seems most people think a girl who's Yandere would want to kill you (which is only true if they have reason to believe you're cheating on them, even OP's pic illustrates this.)
They usually want to protect the person they love.
I assume Kotonoha from school days have given many people the wrong impression of Yandere, since she's famous for carrying around the head of Makoto at the end of the show, but she was not the one who killed him.
I think many who haven't seen the show assume she did.
Kaede from Shuffle, The only time she was shown hurting the protagonist of the show, was during childhood flashbacks, long before she went Yandere, and she never did anything violent after, she just yelled at asa once, who was taking him from her.
Although I've not gotten in the full story yet, Yuno from Mirai Nikki seems primarily interested in protecting the protagonist from others who would try to hurt him.
Point is, it's very unlikely a Yandere will try to hurt you (unless you're a unfaithful pig) but a Tsundere is guaranteed to hurt you, repeatedly, damn near every day.
They abuse their love interests regularly, both physically and verbally.
Tsundere are the ones that are openly violent and hostile towards the person they like, not Yandere, and I don't see how you can get that mixed up.