What's the term for the annoying delay between when I press the button on my camera and when it takes the picture?

There must be a name for that, right?

I have an Olympus Stylus, which is great. It just has one very obnoxious feature, which is that you have to hold the button down for 3 seconds in order for the camera to take the picture. It takes so long that my subjects often move out of their poses because they assume the picture has already been taken.

So, when I’m searching through camera stats, what should I look for? I want a camera that takes the picture instantly, like my friend’s Canon.