BlitzBasic started on the Amiga and was used to create games such as super Skidmarks 1 & 2. It featured easy to use GUI functions that allowed lots of people to create programs for the Amiga easily. The Windows version is known as BlitzPlus and also has GUI support among other functions such as networking, DLL calls, Sound, etc. It is mostly used for 2D games but you have to render rotated sprites before you can use them. It is a procedural language.
Blitz3D includes 3D functions but it is also a procedural language.
BlitzMax is an Object Oriented language. It also allows on-the-fly rotation and scaling of sprites. Most examples of the Blitz family of languages on the web are for BlitzMax.
There is a Linux as well as a Mac OS compiler for it.
MonkeyX is also from the same company and improves upon BlitzMax. It has several free and paid compiler backends as well as several IDEs. The free version of MonkeyX will compile/export to Desktop executables and HTML5.
DarkBASIC first appeared in the late 90's/early 00's and offered several 3D functions from the beginning. It is a procedural language.
The biggest differences in the base language will be the way Types are declared. DarkBASIC will be much like QuickBASIC while BlitzMax will use the Field keyword to define member variables and the Function keyword to define methods.
BlitzBasic and BlitzMax are about the same language. What BlitzMax provided over BlitzBasic was a direct integration with DirectX and OpenGL, which allowed you to make 2D games with hardware supported rendering.
Your average BlitzBasic "Hello World" would usually take up 50% of the CPU.
Just trying to figure out the differences.