Hard reset: Settings | About | Reset Your Phone | Confirm twice. Then the phone will reset back to factory settings. This is the only one that should be called a hard reset. Also referred to as a factory reset by some.
Cold reset / warm reset / restart....... This is where things get fuzzy. Different people mean different things. I'm not going to give them names because of that.
First, simplest. Press the power button and hold it, slide the lock screen down. Phone says goodbye, and shuts off. You turn it back on.
Second, for use when the phone freezes and that one doesn't work. Hold the power button and the volume down button (for Nokia - I don't know if this works on HTC or others, or if this is a Nokia hardware feature). Phone restarts.
Third, power the phone off as you did the first way, but don't turn it back on. Plug in power, and at the same time hold down the down volume button. Hold it until an exclamation point appears on the screen, then let go. Phone will restart. I've seen this posted as direction from Nokia engineers to attempt to resolve the issue of phones shutting off or rebooting. Not sure if this one works on HTC or other hardware, or if it is a Nokia feature.
Hope this helps clear things up for you.