The Para has a TRS loop that requires a special Y-cable that functions as "send and return" on one plug.
TRS Y-Cable at MF
This allows you to run your pickup into the preamp and then through the effects and back into the preamp/DI to deliver to the house. Some effects really benefit from being in the loop of an amp or preamp, depending on what they are or their impedance requirements. At the least, it lets you condition your signal and then add effects to it before sending to the house. The Para has a streamlined approach with the single port and requires a send/receive cable whereas other units have separate send and return ports. The Para has a lot of features for something that can run on phantom.
Regarding the JDI, it has a "thru" that can feed an amp or other effects, if you wish, but it won't loop back into the DI. The JDI is great but is a simple and passive DI, so the Thru might be used to send a signal to your amp or stage monitor. For instance, Lindsey Buckingham uses Rennaissance acoustic-electrics on stage with Turner Wavelength pickups. He send those straight into his DI for the sound guy to handle and then runs the Thru line to his stage amp for monitoring.