Flat screen: The screen itself is flat not curved like older CRT TVs.
Flat panel: The TV itself is flat shaped like an LCD computer monitor. The screen of a flat panel is always flat itself given the technology that is being used.
Note that flat screen and flat panel are two different things. Flat screen will take up much more space. A flat panel can have a flat screen but a flat screen may not necessarily have a flat panel.
Wide screen simply refers to the aspect ratio (ratio of height to width) of the TV. A screen that is much wider than it is tall will typically be called “wide screen”. Whereas, a TV that is square would not. I should point out that the square is the most efficient geometric shape so you actually get more screen area in a square TV than in a wide screen rectangular shaped one.