MPIDE is a fork of an older version of the Arduino IDE with internal pieces changed to support chipKIT. For example, it comes with the chipKIT C compiler (a slightly modified version of XC32 from Microchip), and a new set of standard libraries that allow existing Arduino sketches to work on chipKIT boards.
The chipKIT development team creates builds of MPIDE each time new features are added or significant bugs are fixed. These are called 'test' builds, and they are meant for developers or users who want to use the latest code, but are willing to file bug reports if a problem occurs.
Once a number of test builds have been used, and the build seems stable and working well, a 'release' build is created. This version of MPIDE is considered relatively stable, with significant amounts of testing, and is ready for broader use.
There are two versions of MPIDE - an older version that has not had the library APIs updated to the latest Arduino 1.5.x API level, and a new version that does. The older one has 0023 in its filename, and the newer one has 0150 in its filename.
All MPIDE versions are stored on Amazon's S3 service. This file is an index of every available chipKIT MPIDE version, in a not very easy to read format: https://chipkit.s3.amazonaws.com/index.html
2015-08-20 - 0150
2014-08-21 - 0023
2015-09-03 - 0150
2015-08-02 - 0023