functions - what is the difference between these definitions?

I define 2 functions:

g[s_][x_,y_] := the gaussian  (1)

g1[s_,x_,y_] := the gaussian  (2)

I get the same answer using g[s][ x, y] and g1[ s, x, y].
So, what is the difference?
Is there some advantage to be gained in definition 1 over 2?