The term "booting" comes from the phrase "pulling yourself up by your bootstraps", describing how a computer, on power-up, must load its own operating system into memory before it can do anything else, without any operating system already running to help it.
Booting therefore refers specifically to the process of starting a computer: the system runs its initial hardware checks, then loads the operating system from storage into memory so that the machine becomes ready for use. This is the meaning that matches the everyday word "starting".
"Restarting" describes shutting down and booting again, which is a related but more specific event than the general act of starting up. "Loading" and "running" are broader terms that can apply to any program, not specifically to the unique process of bringing a computer to life from a powered-off state.
Examination reminder: reserve "booting" for the very first startup sequence of a computer, and use "rebooting" only when specifically describing a restart after the system was already running.