Smart TV's are like Smart phones, they have upgraded features and the ability to play apps and integrate with the internet. Some have full operating systems.
HDTV is high definition. HD is 720p to 1080p resolution. Newer TVs are UHD or 4K which are 2160p resolution. Currently 1080p is the bare minimum, I would prefer a high end 1080p to a low end 2160p tv. But if you can stretch it try to get a name brand 2160p (UHD 4K) tv