But shouldn't it be optical on one side and terminate into 1/8" on the other so I can plug into the JB3? That's where I get confused, do I need to get an adapter or what?
Yes and yes. I
think the AD-20 has an optical mini output. And the JB3 has an optical mini input. So if you have an optical cable with two toslink ends (like the one pictured, below), you'll need 2 toslink > mini adapters. Some people like toslink > right-angle mini adapters, others prefer the straight adapters. Of course, if the AD-20 has an optical toslink output, you'd only need one adapter.
FWIW, I've had great results with my Sound Professionals optical cable - right-angle toslink on one end, right-angle mini on the other (no adapters required). It doesn't appear terribly robust, but I take pretty good care of it and always have a backup cable / adapters just in case. An identical cable is available on EBay every so often for ~$10.