The "Live" images are intended to be run standalone, no-installation-required.
From the Debian CD FAQ:
Is a Debian "live CD" available?
Yes. A so-called "live CD", or more precisely, a "live system", is a complete system prepared for a DVD, USB key or other medium. You do not need to install anything on the hard drive. Instead you boot from the medium (DVD or USB key) and are able to start working on the machine right away. All programs run directly from the medium.
The "current" images, on the other hand, are intended for installation to the internal HD. That means that they include far more optional packages, most of which you won't need to install.
From your "current" link:
There are lots of files here! Do I need all of them?
In most cases it is not necessary to download and use all of these images to be able to install Debian on your computer. Debian comes with a massive set of software packages, hence why it takes so many disks for a complete set. Most typical users only need a small subset of those software packages.
Initially, you will only need to download and use the first image of a set (labelled as debian-something-1) to be able to start the Debian installer and set up Debian on your computer.
You could use the live CD for a full installation -- you'd just be starting with a smaller set of pre-downloaded packages. See also Is it possible to install a Linux desktop environment from a live CD?.