HTPC = Home Theater PC (doesn't have to have tuner)
Media Center PC
Media Server (or File Server if not connected directly to tv)
PVR = Personal Video Recorder (if you have tuner card)
DVR = Digital Video Recorder (see PVR)
They are pretty much all the same thing. A computer hooked up to the tv with optional tuner and IR receiver of some sort.
A home theater PC (HTPC) or media PC is a convergence device that combines the functions of a personal computer and a digital video recorder. It is connected to a television or a television-sized computer display and is often used as a digital photo, music, video player, TV receiver and digital video recorder. Home theater PCs are also referred to as media center systems or media servers.
The general goal in a HTPC is usually to combine many or all components of a home theater setup into one box. They can be purchased pre-configured with the required hardware and software needed to add television programming to the PC, or can be cobbled together out of discrete components as is commonly done with Windows Media Center, GB-PVR, SageTV, Famulent or LinuxMCE.