Although some people use the words interchangeably, a "reboot" is a more serious affair than a "restart". A restart is a routine thing. Your computer is in good working order. Before you go to sleep, you turn off your computer. In the morning you start it up again ("restart").
When the word "boot" came into use for computers around the 1970s, it meant a startup from a clean operating system. Use the word "reboot" when something has gone wrong. For example, suppose you just upgraded from System 92 to System 93 and all of a sudden nothing is working right. It's time for a reboot. You would say "Uh-oh! We need to reboot from System 92 and keep using it until they fix System 93".