More or less, Piggy.
A "cold boot" is when you switch off completely and switch on again.
A "warm boot" is when you key something like "control/alt/delete" while the machine is still running.
The term 'boot' comes from the phrase 'To pull oneself up by one's bootstraps' meaning to better oneself. When you boot a computer, it loads the operating system into memory, giving it capabilities that it didn't have before. It has bettered itself.
Rebooting will occur if you simply turn off and on but it does not mean that literally. As radagast says Booting comes from the early bootstrap loader from the phrase to pull up by the bootstrap. On the main disc there is a boot sector and that contains a very simple small program that loads the OS into memory and executes it. The tidy way to reboot is to do start - restart from the start button.
//"A "warm boot" is when you key something like "control/alt/delete" while the machine is still running. // - CTRL-ALT-DELETE is not a reboot warm or otherwise, it's a supervisor interrupt. That say pause what you are doing I want to do some things, eg cancel tasks etc.