Schematic Symbol Help Possible Antiquated JFET Symbol Conversion
I've never seen a JFET be symbolized as such, honestly. But I did look on Google for images of this MPF102 JFET and this is what I found.


As you can see, the symbol matches the second JFET symbol for the J113 JFET. I believe the confusion that you're having is that these transistors will look differently on a schematic, which is not true. However, I believe that the symbol that you're seeing with the MPF102 is different because it's either an older schematic or that's how the software defines how JFETs look.

In terms of particular JFET devices, they will all look the same on a schematic diagram with the exception of the component name on the schematic (assuming that the doped channel is the same, N-Channel, P-Channel, etc.). The pinout of the transistor is going to be the same as well. In other words, with respect to schematic diagrams, the MPF102 and J113 will look the same and will have the same pinouts.