Here's an oldie but a goodie.
The names "Blue Box" and "Yellow Box" come from this architectural diagram of Rhapsody, hammered out hastily in January of 1997 by the merger team:
blue-yellow.png
So when you hear of these colored boxes, remember that they're literally just orthogonal polygons on this chart, and don't refer to packages or virtual machines.
Within Apple, there was a tradition of referring to the current API with the color blue, dating back to the Blue/Pink brainstorming session of 1988 (http://basalgangster.macgui.com/RetroMacComputing/The_Long_View/Entries/2010/6/30_Blue.html) that defined System 7 ("blue") and Taligent (https://en.wikipedia.org/wiki/Taligent) ("pink"). It also helped that blue was established as the color of the Finder logo in the mid-90s.
Why did NeXT get saddled with yellow, a color not usually associated with their products? Perhaps it was an attempt to color-coordinate along CMYK or RBY primaries, assigning the new technology with the color least similar to Taligent or the incumbent Mac API. When the term was first used I can only assume it sounded like it had something to do with Sun hardware, which is occasionally called both "blue hardware" and "yellow hardware" (on account of the Sun logo and the color of sunlight, respectively.)
As far as I know, though, no one ever spoke of Java on OS X as the "Purple Box;" it was just Java for OpenStep and/or Rhapsody.
The above image is a screenshot of /NeueHorizonte/Rhapsody/archdiagram.html from this CD (http://cdrom.nextcommunity.net/compilation/NeueHorizonte_Dec_96.7z), which is a valuable time capsule of what the NeXT ecosystem was like at the time of the merger, and highly worth perusing.
I always love how much they try to squeeze Java into everything during this period. Java was so popular that an OS not having it was seemed as a death wish... so they shoved it in everywhere... and then it basically got no use and was later silently abandoned.
It's even how Cocoa got its name. Because Java was such a top priority, they decided to rename the yellow box to Cocoa so it fit with the hot drink theme that is Java.