smooth equation

Greetings,

I have two sets of experimental data.
I'd like to compare them, but the data are not obtain at the same
points.

For example :
Set 1 :
#X   Y
0     0
0.5  0.5
1     1

Set 2 :
#X     Y
0.1    0.15
0.4    0.41
0.62  0.58
0.99  0.99

You can see a deviation of set 2 regarding to set 1.
My idea is to plot them with smooth.

Can we have the smooth equation back for Set 1 and 2 (called SE1 and
SE2)?
Because I'd like to plot SE1 - SE2 to have a graphic of an evaluation
of the differences.

If it isn't possible. Does somebody see a way of doing that? I ever
think of fitting but the problem is to find the good equation, because
I have very different shapes of data.

Thanks!