A GUI is a Graphical User Interface. Windows is a GUI and is the interface which sits between the user and the computer.
Prior to this, on the PC there was only DOS (Disk Operating System) and was text only - and as such was a User Interface, but not a graphical one so wasn't a GUI.
In your programs, any drop-down menus and buttons are part of
your GUI.
An IDE is an Integrated Development Environment and came about because for many years, you typed your programs into a text editor, saved them to disk, came out of the editor and used a DOS command to pass your source code to a compiler. When compiled, you ran your exe.
When programming these days, the entering of code and compiling/running it are all done in the same environment with the click of a button - without leaving the program. The tasks are therefore integrated.
TDK_Man