If you're like me, mixing up things that sound alike is not difficult to do. For example, I can easily mix up chipKIT and PICkit, especially if I'm tired and I'm not thinking well. MPIDE and MPLAB IDE are a close second; they just sound too much alike. So it's not difficult to see that if the names mix you up and you don't really know that much about either of them, you might wonder what distinguishes the two and why you'd want to use one over the other. For a quick summary of the differences between using MPIDE (Multi-Platform IDE) and MPLAB X IDE check out this MPIDE vs MPLAB IDE blogpost by Digilent.
However, I would like to preface that article with the following points. Since MPIDE was ported from the original Arduino IDE, and since Arduino was meant to be simple and easy to use, there wasn't a whole lot of functionality built into the IDE from the beginning. It simply works as an editor allowing you to compile your code and program it to your target board (via the bootloader). Debugging was not built into Arduino IDE, but most people use "printf()" statements and the Serial Monitor to help debug their programs/sketches. Microchip's MPLAB X IDE, however, has always been a debugging environment in addition to being an editor and integrating a compiler.
That being said, good luck not mixing them up now!