You can cut a taper by offsetting the part in the chuck.
Let's do a little thought experiment. Imagine you have a piece of 1" diameter round stock you want to turn down.
Control experiment: First off, let's just chuck it up normally in a centered chuck and tailstock. The stock is concentric around the turning axis. If you turn 1/8" off the stock, you'll wind up with a straight 3/4" rod.
Offsetting the stock in the chuck: Now pretend that instead of using a centering chuck, we put the 1" stock in a 4-jaw chuck and adjust the jaws so that the piece is offset 1/8" towards the front of the lathe. If we take the same cut as before, then at the headstock, we remove 1/4" of material from one side of the rod, and nothing from the other side. As the cut progresses towards the tailstock, it evens out, eventually taking 1/8" all around. We still wind up with a piece 3/4" diameter over the entire length. It is offset, but not tapered. It doesn't matter which direction you offset the piece, as the chuck is spinning.
Offsetting the tailstock 1: Instead of offsetting at the headstock as above, imagine that we offset the tailstock 1/8" away from the front of the lathe (towards the back). Mount the 1" rod centered at the headstock and centered on the offset tailstock. Take a 1/8" cut the entire length. At the headstock, we'll remove 1/8" all around. Moving toward the tailstock, however, the cut becomes progressively shallower. At the end, we remove no material at all. This results in a turning that is tapered, 3/4" diameter at the headstock and 1" at the tailstock.
Offsetting the tailstock 2: Do the same thought experiment as above, but instead of offsetting the tailstock toward the rear, offset it towards the front. With the same depth of cut, we'll remove 1/8" of material all around at the headstock, and 1/4" at the tailstock. The result is a tapered turning, 3/4" diameter at the head and 1/2" at the tail.
So you see, a non-parallel axis of rotation (achieved by offsetting the tailstock) produces a tapered turning. Offsetting the stock but maintaining a parallel axis of rotation does not yield a taper.
I hope that helps,
Eric