Explain the difference between sin^-1(x) and 1/sin(x), Are there different expressions for both these functions?

You have to be kidding. Difference between arcsin and the reciprocal of sine?

if y is a function of z, ie, y(z), then compare the difference between y(z) and 1/z. Yep, they are different. Now consider z to be sinx, and y(z) to be arcsinx

so arcsinx and 1/sin x are wildly differen functions.