MS-DOS 5 EDIT is actually just a stub which runs QBASIC in editor mode, in which all the BASIC-related features are disabled.
Windows 95 EDIT was different, it actually had BASIC removed from the binary. I don't know if it was a rewrite or if they just deleted (or even #ifdef-ed) out the BASIC parts out of the source code.
QBASIC was basically just a cut-down build of QuickBASIC with some features disabled. The TUI part was provided by the "Character Windows" (aka "Character-Oriented Windows", CW or COW) library, a TUI-mode analog to the Windows 3.x API for DOS TUI apps, it was also used by some other Microsoft products such as Word for DOS. It would be great were Microsoft to open source it (although from what I've heard, significant chunks of this stuff have already been included in various leaks of DOS and Windows source code, but it would be nice to have it publicly available in a completely kosher way)