It would be more accurate to ask what the difference is between Android TV and smart TVs. The answer is that although they are both "smart," Android TV is all about the integration with Google, including search and the Play store. HDTV is simply a video definition format; full HD = 1080p (i.e., 1080 horizontal lines per frame, progressive scan). Compare this to the old NTSC standard of 525i (525 lines, interlaced).
Although Android TV set-top boxes are currently available, there are no Android TVs on the market yet.