I believe they're the same.
-- Cold reboot and cold restart (same)
-- Warm reboot and warm restart (same)
Usually people say "restart" when they're doing a warm reboot (Start button, Shutdown, Restart option).
People say "reboot" when they mean either warm reboot or cold reboot, but usually mean a warm reboot unless they actually specify to do a "cold reboot" (power off the computer and start over completely).