I had both problems--blur, and a noticeable lag between pressing the button and taking the picture. As a layman, I am confused on the focus issue. Can't it just

I had both problems--blur, and a noticeable lag between pressing the button and taking the picture. As a layman, I am confused on the focus issue. Can't it just keep the image it is showing me on the display at the second I press the shutter? Doesn't it keep things in focus continually? When I went to buy a new camera, I couldn't find a single inexpensive digital camera that advertised itself as solving these problems. While I certainly don't even know enough to know what I'm looking for, it seems like a marketing lapse that no inexpensive cameras sell on speed as a feature.