A live CD system is installed... on the live CD itself.
Most of the time, we boot our computers from an internal hard drive. The computer's BIOS (or EFI/UEFI, which may informally be called a "BIOS") accesses the drive, loads the operating system's boot loader, and executes it.
It works the same way for booting from drives other than an internal hard drive. Which drives your computer can boot from (without leveraging another layer of software) depends on your computer's BIOS. Essentially all PCs manufactured anytime in the last couple decades can boot from:
- an internal hard drive
- an optical drive, if the computer has one built in
- an external, USB-attached hard disk or similar device (like a pendrive / flash drive)
Many computers can boot over a network (PXE booting), which is as nifty as it sounds but is complicated enough to set up that it's usually not worth it for booting from a single computer. Some computers can also boot from other devices, such as Firewire (IEEE 1394) drives.
Booting from an internal hard drive runs the system installed on it. In your case, that's whatever operating system was installed by your school's IT people.
Booting from a removable disk, like a CD/DVD or USB flash drive, runs the system installed on the removable disk. When you write an Ubuntu desktop ISO image to a USB flash drive, or burn it to CD or DVD (or other optical medium, such as a Blu-Ray), this causes an Ubuntu live environment to be installed on the CD/DVD/USB.
But there are different kinds of installation.
There are differences between an Ubuntu system installed in the usual way on your computer (i.e., what you would get if you selected Install Ubuntu... which you should probably not do on your school's computers), and a live environment.
A live system is designed to run on a very wide range of different hardware. Therefore, installing it (i.e., making the live medium from an ISO image file) does not require specialized steps to identify hardware, enable drivers for it, and perform other customizations. This is why it can simply be "stamped out" from a disk image.
In contrast, while there is such a thing as a disk image for a hard drive (and they're used by backup solutions like CloneZilla and Ghost), writing a generic disk image to a hard disk would not be an effective way to create a normal operating system installation. This is because:
- Where on the disk partitions must be created, and of what size, varies. Some installations, especially (but not only) on servers, have partitions on multiple disks or use RAID or LVM.
- What initial software is installed and how it is configured varies somewhat, mainly with respect to device drivers.
- An initial user account must be created and some files--at least the user's home folder--are named with their username. The user account's home folder is often located on the same partition as the rest of the system.
A virtual machine is different.
Unlike booting your computer from a traditionally installed system on an internal drive, or a live system on a CD/DVD or USB flash drive, a virtual machine does not involve booting your computer at all. That's why it's virtual: it is a computer simulation of a (different) computer.
As Ruslan Gerasimov says, a virtual machine can run a traditionally installed system or a live system. Whether or not a machine is virtual and whether or not it's running a live environment are independent.
There is one important similarity, practically speaking, between a live system and a virtual machine (live or not):
- You can take a live CD/DVD or live USB from one computer to another, and it should work, because it is not specialized to any particular hardware configuration or user customization.
- You can do the same thing with a virtual machine--because even if the OS installation is machine-customized, it's customized to the guest (virtual) machine, which can be emulated/virtualized on multiple host (physical) machines.