The basic gameplay is the same, but there are a few minor differences.
The trackball moves are the same for swinging the club. But instead of rolling the trackball left or right to switch clubs, you click a pair of onscreen buttons up or down to switch clubs. Also, you click the right mouse button for backspin and left mouse button for no backspin.
Another difference is that when you putt in the arcade you can hit the ball as hard as you want, and you'll still go in the hole if you hit it straight. But on the PC version, if you putt too hard, the ball will roll over the hole like it would in real life.