Why do people say “You gave me a heart attack” when they mean “You made my heart skip a beat”?

They are exaggerating.

Just be thankful they didn't say "You literally gave me a heart attack".

They don't. 
"You gave me a heart attack." is something you say when you have been greatly startled or frightened by something someone did. That's not the same as “You made my heart skip a beat” at all. 

The expression is:  "you almost gave me a heart attack."

It's the more polite thing to say, as opposed to,
'you scared the $h!t out of me' (when you did that) etc.. :)

Probably neither is the truth. 

Update: 
A good experiment while connected to an EKG machine. 
Let someone startle you! 
I doubt that your heart skips a beat. 
The heartrate may increase. 

Its a figure of speech and an exaggeration so it isn't taken literally, but it means that they got really startled or scared. Hope this helped :D

Saying that 'you gave me a heart attack' is a deliberate and extreme exaggeration for effect.  They don't mean it literally - they just mean that 'you frightened me a lot.'

Even saying that 'you made my heart skip a beat' is exaggeration, but just a very small one.  Hearts don't really skip beats unless you have a heart defect.  When you're started, it just feels like it's skipped a beat.

Judging by your update, it appears that you don't know what "You made my heart skip a beat" means. It means you felt a sudden burst of romantic attraction toward someone when you saw them.  This bears no relation whatsoever to "you almost gave me a heart attack".  That means you were scared, startled. Like when someone hides then jumps out and shouts "BOO!"

The fact that there are two ways to say something does not mean that one of them is wrong.

Not even that, more like a panic attack.