This circuit is being called a constant current source, how can this be? Since the gate and the source are both connected together their isn't a potential difference between them. Doesn't' this mean that the transistor should be off? Or do I have this confused with a BJT?
As others have said, it's a JFET, which behaves similarly to a depletion mode MOSFET.
For a voltage across the device that is much bigger than than the cutoff voltage (about 2V) the current is fairly constant. Here is a typical curve from the Onsemi datasheet:
So, at Vgs = 0, the current for voltages of more than a few volts only varies from about 3.5 to 4.0mA (+/- 7% or so). However the actual current is poorly controlled- it might be as low as 3mA or as high as 7mA (parameter IDSS on the datasheet).
Since it needs so much forward voltage it isn't all that useful a circuit compared to alternatives. You can buy more tightly specified devices in a two-lead package- they are called current regulator diodes, but they also require a lot of forward voltage to regulate well and have never been very popular so they are expensive.