With the Tangent continuity option, the extrapolated section will be straight (flat).
With Curvature continutity, the extrapolated section may be flat or curved. (In your example above, it looks like you have a ruled surface. So if you extrapolate the top or bottom edges, the extrapolated section will be curved to match the radius of curvature at the edges. But the left or right edges will be extrapolated flat since the surface has 0 curvature in the ruled direction)
It's easier to understand if you extrapolate a curve.