A priori none except that one is used in volume and the other in surface. (if I understood correctly, one of the two doesn't need a closed outline to work).
The Smoothed and Boundary functions are available in both surface and volume!
The Smoothed function allows you to create volumes or surfaces from multiple sections, and the Boundary function allows you to create volumes or surfaces from multiple sections and several direction paths!
Basically, the border is a great Scan function....
In addition, it is possible to control the junctions with adjacent faces!
I hope I've been clear enough, otherwise I can give you an example!
On the left, the Smoothed function obtained with only two sketches (upper and lower) the function is obtained by sweeping a line between the two.
On the right, the Border function obtained with the same two sketches (upper and lower) in direction 1 and 4 other sketches (lines, arc, etc.) in direction 2 to define the link between the two previous sketches!