The methods are different and will not give the same results. The curve fit will fit a line (one and only one) to all your points (linear least squares if you don't specify anything else) and the extrapolation will be points on that line.
Interp1 will draw a line (provided you use the default option) between succesive points and use that for extrapolation. Therefore you end up with many segments and not a single line.
Cheers!
