DOS program versus DOS console program

I would like to know what the difference between
a DOS application and a DOS console application. I was under the impression that they were the same thing. Is this just a matter of where I execute the code? For example, when I boot into DOS from Windows 98, I launch a DOS session and can run DOS applications; when I open a DOS window in Windows I am running a DOS console window and can only run DOS console applications. Is this what the difference is?

There are a lot of codes which the console cannot run and there are also codes that DOS cannot run.

Consoles dont allow hardware related DMA.

When I reboot into DOS mode from Windows am I in a pure DOS environment? If I am in a pure DOS environment why can't Microsoft Visual C++ or Borland C++ Builder produce programs that run in this environment?

Same reason gcc can't - they're not DOS compilers. If you want a good one, try DJGGP.